This is a really late reply, but I was looking for a solution to this problem myself. Some trial and error revealed that it had to do with the cable I was using. I'm thinking you might have the same issue.
Some net research suggested that poorly shielded cables caused this problem. The cable I was using was a cheap one donated to my brother int he dorms in college (along with a bunch of games. We have no idea who owns them, but they stole our rumble packs).
I had a couple other N64 cables laying around, so I tried the one I'd bought from Gamestop. It's a heavy duty multi-system svideo/composite cable. Switching to that one from the flimsy inexpensive one solved my problem. The black checkerboard was gone and I was shocked at how much better the image was over composite. It's almost like night and day.
My research has suggested that while cables are a likely culprit, some HDTV's might be the culprit too, though this is not the case for me.
Best of luck!
Edited by Lendorien, Fri Jan 2, 2009 12:41 AM.