New PSU seems broken

I recently assembled a computer and it frequently crashes. No blue screens but complete shutdowns; sometimes it will not post (no beeps). After searching a lot I finally figured the problem is power related but nonetheless it is weird and I wonder if I am overlooking something.

Using a multimeter, I:
checked the voltage on the +12V and +5V rails when it does not post; both are below the limits.
checked the voltage on the +12V and +5V rails when it does post and both are fine.
checked the AC voltage. Voltage is a bit low at times (210~V) but within European regulations and the psu specifies it can handle 100-240~V input.
checked if there is propper ground in the room: there is a current when connecting ground and one of the other wires.

The crashes/post failures are appearing completely random, ie I can play skyrim for two hours with no problem and other times it shuts down while idle or doesn't boot at all. Naturally I checked AC voltage when there was no post; it was fine. There is a delay between turning on the pc and me grabbing the multimeter of course, however I would expect that if a brownout were responsible, the psu would stabilize after the input current corrected itself. Such is not the case: if it doesn't provide +12V then it will not until I disconnect it from the outlet and reconnect it again.

The irreproducibility is annoying. If it would never work, I could be certain the psu is broken. Working 90% of the time, it might be hard to prove that it is indeed broken; I assume this is also why it managed to pass quality control checks.

As for relevant specifications:
550W psu
amd phenom II 965BE (stock cooler no overclock)
amd radeon hd 6850
1 hd
1 dvdrw
2 case fans
1 cardreader

You don't mention what type of psu it is you have. There is a somewhat common problem with HEC made units that is like what you describe. If such is the case, then there is nothing to do but replace it.

ADATA BN 550
Apparently that company is supplied by HEC...