Hi, no problem here surely is a forum to ask for some 6502 hardware debugging help, although here it is more general.
You might want to have a look at the VCF Forums:
http://www.vintage-computer.com/vcforum ... -Commodore
or ask the CBM hackers mailing list
http://www.paradroid.net/cbm-hackers.html
Some general PET information actually is on my PETindex site:
http://www.6502.org/users/andre/petindex (links to schematics under "boards").
Now, looking at your coutube video...:
First I think the blue cable that goes to the push button under the monitor looks as if someone added a reset switch - which the original PET lacks. One of the blue wires would go to ground, the other to the CPU's RESET line. The capacitor is to avoid signal bouncing.
The garbage on the screen shows that at least a lot of the system seems to work, namely the power supply, timing, video generation logic (this old PET has the video timing hardwired) and even the screen. Is this garbage screen constant? Or are the characters changing over time?
There is one thing that these PET are known for - you can try to take the socketed ICs out of the sockets one by one and reseat them. The PETs are known for the chips coming loose and reseating helps here.
If that does not work, to check what is broken you would need to do some measurements on the signal lines. I don't know how much you know about electronics and how much experience you have. Maybe it's better to ask someone on the VCF Forum or the cbm hackers list who lives close to your place to have a look.
André