Fixing a HP 38C

[Dave92F1]

I picked up a 38C on eBay for parts, but to my dismay it almost works so I can't steal parts from it - instead I have to fix it.

When I turn it on, it works properly about 1 attempt in 20.

The rest of the time it does something unpredictable - sometimes a blank display, other times all zeros (0000000000), other times random segments turn on and off unpredictably. And sometimes the display is messed up but if I press a key it starts working properly.

I don't think it's the power switch - I cleaned it, and it does the same things if I switch the power externally.

I suspect the power supply isn't starting up cleanly each time.

Any suggestions? (I'm quite handy with a soldering iron, but not really an analog guy.)