I also hope that you will manage to fix this meter! The electronics as such seem pretty robust to me, so I think there's a good chance that the defect turns out to be a fairly simple one. But simple defects can be hard to find.
Apart from the solder connections themselves, I'd verify that the wires have integrity and aren't internally broken (you can't visually see this by looking at the wire). You'd have to open up the metering head for this as well. I never did that on my meter I think, as it wasn't necessary for what I wanted to learn. I'm sure it can be done though, without damaging the unit.
If you end up opening the measurement head as well, please try to take some photos and post them here, if you will. Someone else might find it useful. Also if you manage to solve the defect of course!