A friend and I just dug up an old SNES and are having some trouble with actually getting it to work. 
Using an AV cable, we have it tuned in and the console is on blah blah. BUT all we get is a black screen, i've been reading across the web that its probably a problem with the AV cable, but given the GB community are significantly smarter than most, I was hoping someone could help us out.  
We've blown the cartridge and insert slot by the way, so we don't think cleanliness is a factor. 
Cheers for any help 
x

do you get any sound?

Nothing at all

You do know blowing into the cartridges is a bad idea, right? Well okay EVERYONE does it but what were we to know at the age of 6?

yeah it sounds like you should try a different cartridge. some dont start well and all you get is a black screen. does the screen pop when you turn it on? i mean, do you get a little band of fuzz for a split second?

Of course try other games if you have other games and if not try to ebay a new wire, if these 2 things don't work most likely it might have broken.  If you had the thing stored in a really hot or really cold place the thing could easily have broken.

Do you have an RF adapter available?

Make sure you have a controller plugged in. Some NES, SNES, and N64 games refuse to start up if no controller is present.

I say just keep trying it, taking out the game and putting it back in again, and trying again. Mine doesn't always start the game up and the screen stays black. But if I take it out and reload it, it usually works.

I had a really weird trick that worked sometimes and it might work for you - try putting the cartridge in the refrigerator for an hour. Not kidding. 

 First, find a friend with an SNES and borrow a game that he's certified works. Check if your console plays it fine or not. If it's alright, your game is broken. Clean the connector, and if that doesn't work, pop it open (you'll need a special screwdriver bit) and clean all that, too.
 
If it isn't the game, clean all the connectors in the SNES itself with compressed air. If that doesn't work, wipe them down with a credit card wrapped in a thin cloth (glasses cleaning cloths work very well, I've heard. I don't have glasses, so I can't affirm this. I use a cotton T-shirt). If that doesn't work, wet the cloth with isopropyl alcohol and wipe the connectors down with that (still wrapped around the credit card. To get those little connectors on either side, use a card you no longer need or one of those bogus cards with the white backs and "JOHN M. CARDHOLDER" written on the front you get in the mail with the credit card offers, and snap a bit of it off to reach in the smaller holes) Be sure if you use isopropyl alcohol to give the thing quite a while to dry before you try it.  
 
If none of that works, it's probably not the connectors and you have to take the system apart to figure it out.