oh there you go...
now i know what you're talking about...
something similiar like this happens to my N64, especially if i don't play it in awhile.
first things first get a can-of-air from your local mega-store or computer place (don't use an air compressor because they often shoot out humidity and/or oil)
and blast the hell out all the vents. Dust = bad.
secondly. what i do (and it always works) is, turn off the N64, and take whatever game you want to play, insert it and remove it quickly about 3-5 times.... firmly. but take care to move it correctly in and out (you don't want to damage the game or the connectors) then slam it in (figuratively) one more time and try turning it on....
this works for me. i know it sounds like a voo-doo ritual. but what i'm believing happens is oxidation collects on the connectors in the N64 port, and unless you take the bridge out, and scrub them with a solvent (which i do not suggest you do) there is no other way to clean them properly. even doing so with a q-tip is only just really doing nothing.
moving the cartridge in and out a few times removes the micro-corrosion, effectively using a game cartridge to "sand" the surface clean. and that makes a good connection... well not really sanding, more like buffing. so don't let that word scare ya.
its like using aluminum foil to buff chrome. good stuff