It was the PSU.
The reason i suspected static-electricity to be the cause, was the heartbeat-noise. i assumed (erroneously) a malfunctioning/non-functioning PSU would either cause the machine to not start at all, or show some other consistent behavior.
I replaced the psu with another one, and things are looking good. i still have to run the system thro a few tests, but all signs point to the PSU.
I also posted this question on tom's hardware forum, and got some interesting answers (especially the one about checking OS logs) - http://www.tomshardware.com/forum/382875-31-static-electricity-problem