Burning problem with my cool Dell Optiplex GX270 (XP PRO)

This computer is running nice, cool and totally silent on a 2.80 ghz and 1 gb of ram it's fast and reliable,
but lately it blacks out,
and turn itself off suddenly!
But only while I'm burning stuff on my Sony DRU 510A external USB DVD R-RW.
I'm using Nero 6 Ultra (totally updated).
I've uninstalled Nero and reinstalled it, but this problem is still,
I've tried different media,
I've checked the mobo for bulbing capacitors,
and found none.
I tested this drive on 2 fast 2+ghz laptops of mine,
and my old Dell Dimention 800t test Rig,
I've burned large files up to 4.5gb on Sony DVD media without any issue.
On the Dell GX270 before burning I did disable background running apps the like of virus scanner, firewall ad aware etc etc, and still no luck.
What's puzzling is that this PC was burning well and without any problems,
just 1 month ago it started faltering gradually,
up to the point that I don't trust it anymore.
I'll pay a billion thanks :) to anyone that can help on this issue. :( :(

Dell's brag sheet might show the cause of the problem:

Quote:

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Power Supply:
Small Form Factor 160W
Small Desktop 210W
Small Mini-Tower 250W

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Frankly, if that's for real Dell is really cutting corners. I've got more powerful PSUs in eight-year-old HPs. I'd test the PSU first.

If you have, or can borrow, a multimeter, here's how to test a power supply:

Testing PSU voltages

Or alternatively you can buy a proper PSU tester, they don't cost much:

PSU Tester

ATX12V PSU Tester

I'll buy a PSU tester today at Fry's electronics and report back my findings.
Supper, and Igbpop, Thx a billion for your hints and links!