The PSU shouldn't affect write quality, your motherboard would be blue-screening and hanging long before stuff like that was happening.
Have you tried using the drive in a different PC, or using a known working drive in yours? It is possible, though unlikely, that you've had two defective drives. The LiteOn can throw a wobbler if the PSU current is too low, but it usually complains by throwing the tray out every time you switch on.
The media shouldn't be the problem, but try writing at 4x, and see how you go there.
Also try copying a disc by reading in from the LiteOn to your HDD and back again, rather than on the fly from your CDROM drive.
My personal theory is that your IDE channels are malfunctioning somehow. Try disabling UDMA in your BIOS (set the LiteOn to PIO mode 4) and / or setting your IDE drivers in Windows to the Microsoft defaults.
BTW the last sector in CD-Speed Scandisc always comes up red. Nothing to worry about