Were you able to diagnose what's wrong with your ZX81? Usually it's a simple problem, it just takes a while to diagnose.
BTW, if you do want to get rid of it at some point, it would be nice if you could sell it on ebay or locally. The number of ZX81s left will just keep going down and they are quite decent for learning about electronics/digital systems.
I loved hacking Sinclair machines. I still have my first ever ZX Spectrum, complete with holes in the case and reset button mod.
The ZX printer brings back memories too. I remember naively printing the source code for a game I created only to come back later and find it completely faded and unreadable.
It is rather better than my homemade one from 1982
https://twitter.com/njcw/status/1368566103933337603
My dad gave me a old keyboard from something and I traced the zx81 PCB to discover how it was wired, then rewired the new keyboard the same.
I connected it by burning a hole in the case with my soldering iron to poke the wires through!
It was a dream compared to the membrane keyboard.