The 550w wasn't NEARLY as good as the 650w either. If I remember correctly, it was only actually capable of around 450w peak when it was new. Couple that with the fact that its a 5 year old unit now, its not going to be anywhere near what the sticker says anymore.
I'm telling you, that PSU is likely the cause of your problem. I had a few of those units. Great bang for the buck 5 years ago. Again, I'm honestly surprised that your 8800's work on it at all. But the 5830 does draw more power at startup than your 8800's do.
The TP3 550w only had 500w PEAK POWER on the 12v rail to begin with. Not continuous...but PEAK. And that was 5 years ago.
Damn! Well this give me an excuse for the wife to head to micro center tomorrow. I am thinking a 700W PS. What are good low price range models? I heard Corsair is good but expensive.