Thanks for your reply! I managed to disassemble it to have a look at the MOSFET and it looks like it's IRF3205 which according to a datasheet I found online has VDDS of 55V, so they should have survived it, shouldn't they?
I'm quite surprised that it's such a common and cheap MOSFET, I thought they'd use some weird, hard to get part... I could replace this quite easily...
Anyway, what is the other most likely part to die? Probably some diode?
EDIT: Found out that the two big 3300uF capacitors are directly across the battery terminals and are rated only for 35V, could they be the issue? They are not bulged or visibly damaged in any way. But they are quite easily accessible so I might try to replace them anyway. It's probably worth the shot as I can't find anything else. The only other thing that seems to be shorted is a big ER5D diode, but it's supposed to withstand 200V (140V reverse) so I can't think of an reason why it should fail...
But I'm gonna leave it till the morning, so I don't make another silly mistake...