A PET is available with two (2) different types of video circuits:
1. Without a Cathode Ray Tube Controller (CRTC) chip.
2. With a CRTC.
The former type will give a random display (as you have) on power-up. This indicates that the majority of the VDU circuitry is working.
The problem is either the CPU not working (no clock, no reset, or a faulty CPU), the CPU halting (due to faulty ROMs or the inability to select or read the correct data from the ROMs), or the inability of the CPU/ROMs to successfully write data into the video RAM.
We have to be quite religious, in this case, identifying what the issue could be, by ruling out what it can't be.
If the PET has a CRTC, the likelihood is that the screen will be black on startup due to the requirement for the CPU to program the CRTC to get anything sensible out of it.
Since you are having problems measuring things on the data bus, can I suggest reverting to my PETTESTER, and we can work through the potential scenarios one at a time?
Let me know when you have done this.
Dave