[SiriusHardware]

Yes, you are going to have to get to the bottom of that power problem before you can seriously tackle anything else.

Random stuff on the screen is (counter intuitively) a sign that your screen RAM and display hardware are working normally, but the main system is not managing to clear the screen, one of the first jobs it usually does.

Do you have the means to program EPROMs? There is some test code which could be very useful to run at this point but it needs to be programmed into an EPROM.

UD6 and UD7 are PROMs and PROMs CAN run quite hot in normal operation although I can't say whether yours should. One of the jobs the test code I mentioned does is to checksum the PROMs, which gives a useful indication as to whether they are OK.