my advice is try and get another psu as checking the ps3 for current is very dangerous. on top of that i think you covered every other possibility, it really does seem like a psu problem. anyway try and get a new psu because unless you like 20-30 amps of current going through your body (thats enough to kill) its actually not worth it.
silly question - is your fan inside your ps3 working?
if you insist on checking your own psu then you need to remove it then attach a crocodile clip to the metal outside and join the other end to the ps3 shielding metal then get a bit of wire and attach one end to one of the metal prongs on the ps3 (avoiding shorts) and the other end of that cable where the prong fits in the psu then for the other side attach positive lead of multimeter where other prong would go and attach negative lead to the second prong on the ps3 mainboard (all connections should be secure as if any slip it may fry your machine worse than it is).