Well the few chips are a common op-amps and logic chips, and I'd find that PCB the perfect size to work on, and the traces should be pretty easy to figure out. Personally not being familiar with such circuits, I'd start making a schematic in a simulator, just for layout, labelling, and sim of any circuits I could.
The RTH is probably a 1.5k thermistor, I don't see it tho. Was it in series right after the input ? I've seen that on a DMM, with a fuseable 1k resistor before the 10Meg
If you are lucky, it's not a MCU problem. If it is tho, I hope it's not some black tar covered MCU that can't be replaced. But if you could find a replacement, it still probably needs the firmware and maybe calibration settings.