800 Ohm or so for +5V-gnd and 4Mohm for 12V-gnd, so OK I guess ?
4 MegOhm isn't right, way too much resistance -- I'd guess you didn't get the right test point or a good connection. On a sample here, +12V to ground is about 59 KOhm. +5 to ground is about 500, close enough to yours that I'd not suspect it.
My PS actually does not click. The power just shuts off after one second or so. So perhaps not a short ?
Ah yes: no. If there is a short, the PSU will click as the over-current protection kicks in, then resets, repeatedly. No clicking very likely indicates the problem is not a short.
Presumably then the COPS power control circuit is telling the PSU to shut off.
Refer to sheet 2 of the 5 page schematic...
Check the ON signal at U7F-12.
If it is low, then that will turn off the power.
I see that "ON" is pulled up by R42 to "+5B2" which came up earlier, so re-check that +5B2 is roughly 5V.
Presuming that "ON" is low and +5B2 is around 5V; pushing the power switch should make "ON" go high... does it go high briefly or stay low?
Depending on what you find, work back through the circuit to the COPS and see if it is generating the ON state or not, and/or see if some other part of the circuit is over-riding that.