00-04 cars (maybe even 05) had an issue with the brake pedal sagging and not fully coming up. Depending on how this is adjusted it may not be releasing pressure. The factory eventually figured this out and installed a spring to help out. It may not be your solution, but it is a place to start. For now, rig up bungee to pull up on the pedal. At least your brake lights will go off as they should.
But yeah, brakes sometimes always drag a little. At least you should pull off your drums to see what is going on in there. There may be just a bunch of dust hanging things up, or maybe your pad linings have come off your shoes and causing havoc.