Power Supply Question about XP Barton 2500

Currently, I have a 1.5 year old 350W Sparkle power supply. In the PC
is:

Sparkle 350W power supply from other computer 1.5 years old
Asus A7V8X-X
AMD Barton 2500 XP
1024 RAM 2x512 333 corsair valueselect
40GB Maxtor 7200
120GB Maxtor 7200
CDRW
DVD-RW
two larger fans in the antec lanboy case

I have tried three motherboards before I decided it was the power
supply. I welcome corrections.

All mobos kept rebooting. Mostly when I added a second stick of th
512. So, I suspected the RAM, timing, etc. One mobo thought it was
the mem. slot. Finally, on the third mobo, the pc would get "stuck"
not post, nothing. I removed a RAM module it would boot, but sometimes
still fail. I then put two other sticks from old machine that worked
well 2100 256 & 128. Same problem. Hangs, no POST or boot. Finally,
eight year old suggested it was that thing that I put in there from the
other computer (power supply.)

I put the 2x512 333 memory back in. I unplugged one 120 secondary hard
drive. The system booted, almost every time. I then took the lead
that was plugged into the 40 and put its extra power lead on the 120.
It booted again. Maybe that separate lead was bad?

In any case, I believe it is the power supply. What should I have for
the system? Evidently, mine isn't good enough. Any other suggestions
are welcome. Thank you for reading this longer post.