when I bought my DK, it would freeze up after the high score screen when it goes into gameplay during attract. few power cycles later, all I got were 0's. I don't even remember where I saw it, but I read that had something to do with the Z80 CPU, so I disconnected everything (it's a 4-board, no edge connector, have to connect like 14 cables I swear) and went through the strenuous task of pulling all the boards out of the pushpins. (a bitch, I might add)
I started pulling every socketed chip, particularly the CPU was covered in corrosion on the legs. I tried an eraser first, then got fancy with some sandpaper. after doing that on every poo-pooed chip, I put it all back together and sure enough, the game worked fine.
now it locks up intermittently. nothing with a blue screen, but I would suspect that considering I just cleaned mine not but 1 month ago and already it's doing it again that it could be the same cause.
if you go that route, make note of the CPU's orientation. there were no markings on mine to designate which was the "keyed" end. I luckily had a spare 2-board set with the deal to use as a visual aid there.
EDIT: just out of dumb curiosity, is it running the original Nintendo power supply? mine has a switcher mod, I was just wondering if that would be another factor.