I picked up this PET and trying to restore it. Screen is garbeled on boot and stays like that displaying random chars, some of them flashing. Tried to resocket the chips, but it didn't help. I don't have a logic analyzer, and ram chips are not socketed. What sort of checks I can I do to identify the fault? I have a multimeter and osciloscope, not very skilled at electronics, though.
The garbled screen is normal on startup, but should be replaced by the BASIC screen after a moment.
There's a rather detailed troubleshooting guide, including links, at http://www.dasarodesigns.com/projects/troubleshooting-common-problems-with-the-commodore-pet-2001/
I'd suggest that you ignore the spare parts sales pitch at the beginning and work your way through it.
You might also want to have a look at the Tynemouth Software PET repair blog entries at http://blog.tynemouthsoftware.co.uk/ -- they show fixing some interesting PET issues step by step.
This is anecdotal, so take with a big grain of salt...
I have a C-64 power supply that was home-brewed for me by my Dad when I was a kid from the remnants of the original. My Dad, never being one to do anything halfway, did a fantastic job and added a 'voltage adjust dial' and analog meter to the finished supply. This means I can actually dial-down the voltage to my C-64 until the computer does _weird things_™.
Not that I do this on purpose, but occasionally the dial gets bumped and the volts go low and the C-64 breaks out into a screen of gobbledy-gook that looks almost exactly as you describe.
I'd check the power supply first thing and make sure there are enough jolts going to the main board.