Based on feedback from a number of people and some developments since this was first posted, here's an alternative version of the draft (comments are ommitted except for changes; changed picked noted in bold):
Round 1
1. St. Louis (1-15): Jake Locker*, QB, Washington
2. Tampa Bay (1-15): Ndamukong Suh, DT, Nebraska
3. Cleveland (1-15): Casey Clausen*, QB, Notre Dame
4. Detroit (2-14): Russell Okung, OT, Oklahoma St.
5. Oakland (2-14): Gerald McCoy*, DT, Oklahoma.
6. Kansas City (4-12): Eric Berry*, S, Tennessee
7. Washington (5-11): Brian Bulaga*, OT, Iowa
8. Buffalo (6-10): Sam Bradford*, QB, Oklahoma
9. Tennessee (6-10) -> Derrick Morgan*, DE, Georgia Tech
Tennessee gets a powerful pass rusher.
10. San Francisco (from Carolina (7-9)): Rolando McClain*, ILB, Alabama
11. Seattle (7-9): Bruce Campbell*, OT, Maryland
12. Miami (7-9): Dez Bryant*, WR, Oklahoma St.
13. Jacksonville (8-8): Brandon Graham, DE, Michigan
Wanted Morgan, but Jags settle for a disruptive DE with a non-stop motor.
14. Chicago (7-9) -> Denver: Terrance Cody, DT, Alabama
15. Projected trade: Baltimore (from San Francisco (8-8)): Joe Haden*, CB, Florida
Ravens trade up to get the best CB prospect in the draft.
16. NY Jets (8-8): Cameron Heyward*, DE, Ohio St.
Son of Ironhead will be an amazing 3-4 DE. As a Pats fan, I hate this pick.
17. Atlanta (9-7): Greg Hardy, DE, Mississippi.
18. Houston (9-7): Jason Pierre-Paul*, DE, USF.
19. San Francisco (from Baltimore (9-7)): Taylor Mays, S, USC.
20. NY Giants (9-7): Brandon Spikes, MLB, Florida.
With Antonio Pierce having a neck injury, the Giants get an upgrade with Spikes.
21. Arizona (10-6): Sergio Kindle, DE/OLB, Texas
22. Dallas (10-6): Anthony Davis*, OT, Rutgers.
23. Seattle (from Denver (10-6)): Ryan Mallet*, QB, Arkansas
24. Pittsburgh (10-6): Mike Iupati, OG, Idaho
25. Green Bay (11-5): Charles Brown, OT, USC
26. Philadelphia (11-5): CJ Spiller, RB, Clemson
27. Projected trade: Carolina (from New England (12-4)): Carlos Dunlap*, DE, Florida.
Pats trade the pick for DE Julius Peppers. Carolina had no 1st round pick, but gets one of the elite talents in the draft and a potential young Peppers.
28. Cincinnati (12-4): Jermaine Gresham, TE, Oklahoma
29. Minnesota (14-2): Dan Williams, DT, Tennessee.
Vikes get another DT named Williams, a fast riser to eventually replace Pat Williams.
30. Indianapolis (15-1): Travis Lewis*, LB, Oklahoma
31. San Diego (12-4): Arthur Jones, DE, Syracuse.
32. New Orleans (15-1): Sean Weatherspoon, OLB, Missouri
Round 2
33. St. Louis: Everson Griffen*, DE, USC
34. Tampa Bay: Navorro Bowman, LB*, Penn St.
35. Cleveland: Damien Williams*, WR, USC
Browns need help everywhere, including playmakers at WR.
36. Detroit: Brian Price*, DT, UCLA.
37. Oakland: Jahvid Best*, RB, Cal
38. Kansas City: Jerry Hughes, DE/OLB, TCU
39. Washington: Tony Pike, QB, Cincinnati
40. Buffalo: Trent Williams, OT, Oklahoma
41. New England (from Tennessee): Maurkice Pouncey*, C, Florida
42. Carolina: Brandon LaFell, WR, LSU
43. Seattle: Jonathan Dwyer*, RB, Georgia Tech
44. Miami: Ricky Sapp, DE/OLB, Clemson.
45. Projected trade: Baltimore (from New England, from Jacksonville): Demaryius Williams*, WR, Georgia Tech.
Ravens get a big, athletic WR with tremendous upside. Ravens give up their 4th round pick (#115) to move up for Williams, a 1st round talent.
46. Tampa Bay (from Chicago): Donovan Warren*, CB, Michigan
Bucs get a 1st round talent to pair with Aqib Talib.
47. San Francisco: Gabe Carimi,* OT, Wisconsin
48. NY Jets: Brandon Ghee, CB, Wake Forresty
Jets need a CB to pair with Revis. DT Dan Williams could be the pick as an eventual successor to Kris Jenkins.
49. Kansas City (from Atlanta): Von Miller, OLB, Texas A&M
KC gets a Dumervil type OLB to pair with Jerry Hughes. Should create lots of sacks.
50. Houston: Golden Tate*, WR, Notre Dame
51. New England (from Baltimore): Joseph Barksdale,* OT, LSU
Pats get a talented tackle with great feet/power who should do for RT what Sebastian Vollmer is doing at LT.
52. NY Giants: Aaron Hernandez*, TE, Florida
53. Arizona: Aurelius Benn*, WR, Illinois
54. Dallas: Morgan Burnett, S, Georgia Tech.
55. Denver: Allen Bailey*, DE, Miami
56. Pittsburgh: Kareem Jackson*, CB, Alabama
Steelers upgrade their secondary with a potential 1st round talent.
57. Green Bay: Jared Odrick, DE, Penn St.
58. Philadelphia: Jeremy Beal*, DE, Oklahoma.
59. New England: Greg Romeus*, DE, Pittsburgh.
60. Cincinnati: Eric Norwood, DE/OLB, South Carolina
61. Minnesota: Reshad Jones, S, Georgia
62. Indianapolis: Jason Fox, OT, Miami
63. San Diego: Ryan Mathews*, RB, Fresno St.
64. New Orleans: Marvin Austin*, DT, North Carolina.
Round 3
65. St. Louis: Bruce Carter, OLB, North Carolina
66. Tampa Bay: Austen Lane, DE, Murray State
Bucs need pass rushers. Badly.
67. Cleveland: Toby Gerhart, RB, Stanford
68. Detroit: Mike Johnson, OG, Alabama
69. Oakland: Ras-I Dowling*, CB, Virginia
Raiders get a big DB who can play either CB or S.
70. New England (from Kansas City): Corey Wootten, DE, Northwestern
Pats get a 6'7" 3-4 DE who was once considered a 1st round pick.
71. Washington: Kyle Calloway, OT, Iowa
72. Buffalo: Jeff Linkenbach, OT, Cinncinnati
73. Tennessee: Trevard Lindley, CB, Kentucky
74. Carolina: Nate Allen, S, USF
75. Philadelphia (from Seattle): Darrell Stuckey, S, Kansas
76. Miami: Brandon Lang, DE/OLB, Troy
77. Jacksonville: Tim Tebow, QB, Florida
78. Chicago: Marshawn Gilyard, WR
79. San Francisco: Colt McCoy, QB, Texas
80. Cleveland (from NY Jets): Vince Oghobasse, DE, Duke
81. Atlanta: Sean Lee, LB, Penn St.
82. Houston: Anthony Dixon, RB, Mississippi
83. Baltimore: Washington makes plays all over the field. With some size, he could eventually take over for Ray Lewis.
84. NY Giants: Chad Jones, S, LSU
With Kenny Phillips' career in doubt, Giants get a huge FS as insurance.
85. Arizona: Shaun Lauavau, OG, Arizona
86. Dallas: Vladimir Ducasse, OT/OG, UMass.
87. NE (from Denver): Mike Pouncey*, OG, Florida
88. Pittsburgh: Phil Taylor* DT, Baylor
89. Green Bay: Patrick Robinson, CB, Florida St.
With Harris and Woodson aging, depth at CB is needed.
90. Philadelphia: Philadelphia: Jeff Owens, DT, Georgia.
91. Oakland (from New England): Jevan Snead*, QB, Mississippi
92. Cincinnati: Tyson Ayualu, DT, Cal
93. Minnesota: Syd'Quan Thompson, CB,Cal
94. Indianapolis: Jermaine Cunningham, DE, Florida
95. San Diego: Kam Chancellor, S, Virginia Tech
96. New Orleans: Noel Devine*, RB, West Virginia
Round 4
97. St. Louis: Akwasi Owusu-Ansah, CB, Indiana-Pa.
98. Tampa Bay: Chris Marinelli, OT, Stanford.
99. Cleveland: Jordan Shipley, WR, Texas.
100. Detroit: Greg Jones, ILB.
101. Oakland: Cameron Jordan*, DE, Cal.
102. Kansas City: Danario Alexander, WR, Missouri.
103. Washington: Kris O'Dowd*, C, USC.
104. Buffalo: Roderick Muckelroy, LB, Texas.
105. Tennessee: D'Anthony Smith, DT, Louisiana Tech.
108. Carolina: Michael Morgan*, OLB, USC.
Fast OLB with terrific range should be a nice complement to Jon Beason.
107. Seattle: Jon Asamoah, OG, Illinois.
109. Miami: Pat Angerer, ILB, Iowa.
106. Jacksonville: Stefan Wisniewski*, C, Penn St.
110. Chicago: Sam Young, OT, Notre Dame.
111. San Francisco: George Selvie, DE/OLB, USF.
112. Philadelphia (from NY Jets): Eric Decker, WR, Minnesota.
Decker falls because of injury. Nice over the middle big WR to complement DeSean Jackson and Jeremy Maclin.
113. Atlanta: Myron Lewis, CB, Vanderbilt.
114. Houston: Matt Tennant, C, Boston College.
115. New England (from Baltimore): Dexter McCluster, RB, Mississippi.
116. NY Giants: Perish Cox, CB, Oklahoma St.U
117. Arizona: Boo Robinson, DT, Wake Forest.
118. Dallas: O'Brien Schofield, DE/OLB, Wisconsin.
119. Denver: Selvish Capers, OT, West Virginia.
120. Pittsburgh: Brandon Deaderick, DE, Alabama
Can never have enough 3-4 DE depth.
121. Green Bay: Jason Worilds*, DE/OLB, Virginia Tech
122. Philadelphia: Anthony McCoy, TE, USC.
123. New England: LeGarrette Blount, RB
After grabbing a 3rd down back, Pats get a big boomer at RB. A TE like Ed ****son could also be an option.
124. Cincinnati: Kase Keenum, QB, Houston.
125. Minnesota: Zane Beadles, OG, Utah.
126 Indianapolis: Mike Neal, DT, PUrdue
127. San Diego: Desmond Brizcoe, WR, Kansas
128. New Orleans: Adam Ulatowski, OT, Texas.
I'm assuming Earl Thomas and Adrian Clayborn don't come out.
In this version, the Pats pick up an extra 4th round pick by trading with Baltimore in the 2nd round. They end up with:
1(27) Traded for Julius Peppers, DE/OLB
2(41) Maurkice Pouncey, OG/C
2(51) Joseph Barksdale, OT
2(59) Greg Romeus, DE/OLB
3(70) Corey Wootten, DE
3(89) Mike Pouncey, OG
4(115) Dexter McCluster, RB
4(123) LeGarrette Blount, RB
Add a TE and a punter, and they should be set. I still don't know how to make the Peppers money work, but we'll ignore that for now.