Dave S , Aug 25, 2010; 12:38 a.m.
Anya, I bet everyone here is going to say 'Check the battery!'
The AE-1 is strictly battery-dependent. I wonder if the battery was weak when you bought it, and then it conked out and the meter failed, or the electronic shutter failed to trip. It will cost you about $5 to find out if it was the battery-- just get a cheap alkaline PX28 6-Volt cell.
The thing about buying old cameras for use is that around half of them need an overhaul right away, but you're correct that the cost of replacement would be less than the cost of repair. If you're in the U.S., you might look at KEH.com, which sells used cameras at excellent prices, and they have an excellent guarantee policy. I'm in Canada and I've found Henrys.com in Toronto to be outstanding too.
If you get into manual focus Canon cameras, post your experiences on the Canon FD forum here on photo.net-- there are folks there with encyclopedic knowledge of the darn things.