How did you clean the cartridge slot? Maybe you just need to clean it better. If all else fails, you can buy a replacement cartridge connector (like the ones you can buy for an NES) but they're a little harder to find. You can usually find them on eBay though.
I would put my money on a dirty/damaged cartridge connector. If that corrosion was the only thing that looked bad on the board, maybe you can go a step further than cleaning it. You could desolder each leg of that chip, clean it some more, then resolder it. But I would focus on the cartridge connector.
edit: Here's one...
http://www.nesrepairshop.com/online_sho ... SSID=7445a
But be aware, there are a few different model SNES's. And that link states that, apparently, there is a 'plug-n-play' connector and one that has to be soldered on.