Elvis Costello
When Elvis Costello's first record was released in 1977, his bristling cynicism and anger linked him with the punk and new wave explosion. A cursory listen to My Aim Is True proves that the main connection that Costello had with the punks was his unbridled passion.
The Police
Nominally, the Police were punk rock, but that's only in the loosest sense of the term. The trio's nervous, reggae-injected pop/rock was punky, but it wasn't necessarily punk. All three members were considerably more technically proficient than the average punk or new wave band.