Random freeze/restart on brand new build

Hi everyone

I have a brand new homebuilt system

Specs:

Windows 7 RC
Antec Three Hundred
LC Power LC6550GP2-550W/14 V2.2 Silent Giant
Gigabyte GA-MA790XT-UD4P, AM3
AMD PHENOM II X4 955 (not overclocked)
A-Data Extreme 1333+ 2x2Gb CL 7-7-7-21
WD Caviar Black 640GB, 32MB, (WD640AALS)
WD Caviar Black 1TB, 32MB, (WD1001FALS)
Maxtor 250 Gb (ATA133)
SAPPHIRE Radeon HD4850 512MB
DVD/RW NEC AD-7203S-0B SATA

My problem is that it freezes or restarts at random.

My mobo has a 8 pin CPU power connector, but my PSU has only a 4 pin connector. Considering my CPU being quite power hungry (125W) could this be the case, that it's not getting enough juice, eventhough the freeze happens in idle mode?
I have noticed that some people have said that the PSU is the main problem for this sort of behaviour as my PSU is only 550W.
But at full load (Prime95 and Furmark) my system consumes little less than 500W.

I have run Prime95 and Furmark for 7 hours straight and it did not restart nor freeze, but after dropping into idle and at watching movies or browsing the web or stuff like that, the problem presents itself. Could it be that the PSU has problems in idle mode and that fluctuations occour when it's using the least power?

I will be getting a more powerfull PSU (with a 8 pin CPU rail), but want your advice (so I won't spend 100€ on something I might not need)


P.S. My home systems run on an industrial class online UPS (no electrical current fluctuation).

I thank you in advance for your help


Best regards.