It's the 12V TVS diode that's shorted. If you remove it, and the short is cleared, then you should be OK. All other measurements seem OK. At least there are no shorts. (see my edit)
Just retest the zero-ohm resistors. I would have thought that the pair at the left-hand edge would be open while the pair nearest the 5V diode would measure 0.0 ohms. If a pair is open, you can replace both with a single 4A fuse. Otherwise, depending on your skill, you can flow a blob of solder over them. That entails an element of risk, so it would be best if you used an external enclosure with an AC adaptor. These are current limited by design.
Make sure that your PSU is good. Also make sure you are using the cables that came with that PSU. That's because modular pinouts are not standardised.
Edit:
I may have mixed up the diodes because the PCB layout is very strange in that area. Nevertheless, the procedure remains the same, ie remove whichever diode is shorted. You can do this by snipping its pins with flush cutters.