i've heard of this before, in fact, i know someone who formatted the whole drive, reinstalled windows and still got the pop ups! it turned out they had either remote desktop or remote assistance turned on.... strictly speaking this shouldnt matter but it turns out by having one turned on it...
i would say it's the psu that's gone.... i've had a few pc's like this, you hit the on button and the on light flashes and sometimes sounds a quiet clicking noise... all the time i've had this i've replaced the psu and it's worked... dont think the bios would have anything to do with it
the other day someone brought a pc to me because the monitor wasnt receiving a signal from the pc... after all the usual checks (different cables, monitor, tower unit etc...) i realised it must be something more serious. i spoke to an i.t manager who said when this happens, after the usual...
i dont think removing the battery will help... sorry! it will reset the cmos, but the problem is you've upgrading it and that upgrade have overwritten the existing cmos... worth a try though... you only need to remove it for about 10secs, just long enough for the power to drain... if it doesnt...