Hey all, I'm curious if anyone has run into this:

On my NES, everything seems to play fine at first. After a while, the screen will start to fill up with 'garbage', the sprites will turn into other sprites, letters, etc. The games play fine in this state, we even managed to get pretty far in Contra without being able to tell what was what. I haven't busted out the meter yet, but I'm guessing a cap will be the issue. Any ideas where to start?