Well, the last I heard, the major difference between them was the power supply needed, with ATX PSUs having different power connections to the MB (not HDDs etc). To confuse the issue a little, some transition MBs came with both ATX and AT PSU connectors, so one could upgrade older PCs with AT PSUs with a better MB. Generally though they are NOT interchangeable.
In your case, have a look at the PSU connector on the MB (size of mouse connector is not a definitive test). AT's have two separate connectors, with colors RRRWBB BBBlYRO (if that makes sense), ATXs have just one.
You should be able to get a good MB that uses an AT PSU, but most are pretty old now. I upgraded my son's PC about a year ago with a new FIC VA-503 that takes both (I wanted to reuse the 72-pin RAM I had, and the case/PSU), but fastest CPU it would take was a 550 AMD. So it can get a bit tricky.
Really, if you want to upgrade (rather than repair), look at an ATX case/decent MB/RAM, etc and just swap HDD/CD etc etc. Really cheap these days anyway.
Other ideas from others out there?
Bill