By virtue of the fact they're old, game cartridges are normally filthy as hell. Which means sometimes they won't work! Not to fear. If blowing on them won't get them up and running, a chemical fix probably will.
This handy instructional vid shows that all you need - provided the problem is dirt and not something more technical - is a little rubbing alcohol and some cotton swabs to get those filthy, grubby old game cartridges good as new.
I've actually done this before with alarming regularity in a previous job working childcare, where our Nintendo 64 games seemed to be there solely for kids to drip honey, juice and pieces of fruit gunk down. And can report that while it works just fine for cleaning the insides of the cart, I actually found them more useful for cleaning the outside, which on cartridges that aren't black (like the N64) tend to get a lot dirtier and grimier than the insides.
[via Go Nintendo]