I know for Haswell you'll probably need another PSU anyway. Some PSU's have serious problems because the idle power draw is so little that they either don't regulate correctly or simply shut off.
Given the "unclean AC input" history you've told us about, I'd target the PSU first. Get one that's Haswell compatible (yup, they exist) and go from there.
That first thing - shutting off because draw is so low - could that be anything like what's going on now?
Will see what PSUs I can get at my local Microcenter...