The dreaded power harness issue was really for the 002. The 003 line was not known for that issue. I owned 2 003 mixers and 4 003 rack units and none ever had a similar issue(but both my 002 mixer and 002 rack did). Still, the OP has nothing to lose by reseating the harness connections(do each connection at least 5-6 times so if there is oxidation, doing the reseat several times has the best chance of scraping thru any buildup). I'm not sure if each channel has relays, but they might(for switching between mic/line or HPF in/out), so if you find relays(and they are indeed socketed), swap between 2 channels to see if the problem moves. That would indicate a bad relay and replacements are probably available from Mouser or Digikey, or maybe an Avid-approved service location like allproelectronics.com(out of Nashville).
Re moving to a new(er) interface, consider a few things; newer stuff is likely to sound better, firewire is rapidly going the way of floppy drives and the 003 could find itself a non-runner with some upcoming PT release
