Is it a MarkII?
It's very easy for the power switch to come apart from the little pin underneath that actually switches the power on / off, my guess is that's the problem.
It's easy to fix but takes a while. there's a useful page here:
http://www.kult.co.uk/Technics%20SL-1200-1210%20FAQ.htm
with advice about most aspects of keeping them ship-shape. the very last thing on the page is the relevant bit.
if this is what's wrong, you just need to undo about a hundred screws on the bottom and take the rubber base off so you can get inside, and push the little pin back up; i recommend putting a tiny bit of blu-tak on to help it stay put. careful not to hurt the tonearm while the deck is upside down; if you a lid put it on the deck.
if that isn't the problem i'm not sure what to suggest next; can't remember if there's an internal fuse, there probably is...
