Suggest you power the hard drive and CD-ROM drive from the ATX psu for a test. This takes the strain off the A2000 psu. If the A2000 acts normally or falters, then your sure about the power supply being a problem. (Hope that sounds right?).
If you have a voltmeter, add a "Y" power plug so you can check check the voltages on the drive line during operation, and especially when it falters.
The drive connector on the A2000 psu is wired as follows:
Orange Blue Blue Yellow
12VDC---Ground----5VDC
If the A2000 psu is the problem, I would then suggest you remove the power supply, open the case, and clean it. Also check the fan, to see if it's burdened with grim, and actually turns.
Taken from this source:
AMIGA TROUBLESHOOTER - PART 2: A500/A2000
THE AMIGA TROUBLESHOOTER IS COPYRIGHTED © 1993 IAN PERRY.
HTML conversion by Thomas Unger 2002. View the original document.
VIDEO PROBLEMS
1. Screen brakes up (scrambles) after running for 15 to 30 minutes.
Probable causes are:
* 8370 - 8372/8375 U2 Fat Agnus (U101 A2000)
* 8362 U4 (U201 A2000)
* U2 Socket (U101 A2000)
2. System locks up when double clicking icon:
* 8370/8375 U2 (U101 A2000)
* 8362 U4 (U201 A2000)
* 8520 U7 Odd CIA (U300 A2000)
* 74LS32 U37 (U302 A2000)
3. Scrambled video loss of composite sync.
* 8370 - 8372/8375 U2 (U101 A2000)
* 74HC245 U41 (74HCT244 U205 A2000)
* RP403
4. Incorrect colors (loss of red, green or blue):
* 8362 U4 (U201 A2000)
* 74HC245 U40-U41 (74HCT244 U205-U206 A2000)
* Video Hybrid
5. No video (black screen)
* R405 4.7 ohm resistor
* R406 4.7 ohm resistor
* 8362 U4 (U201 A2000)
* Video Hybrid
* 74HC245 U40-U41 (74HCT244 U205-U206 A2000)