Let's try to resolve your issue in a one-step-at-a-time manner.
Instead of jumping over several heads and breaking the brains over the Windows environment, let's first make sure from within plain vanilla DOS that your CDRW is not hardware faulty and the system BIOS has no problems with it. As the drive works fine in another system, likely its HW is Okay. However, you'd need to make things certain on the new system. Only if it passes the DOS environment can we talk about the Windows.
Here is what I'd suggest as the first approach:
1. I'm not positive about suitabily of the ATA-133 cable for anything else but HD connection. Does your MB controller explicitly supports the ATA-133 interface?! Does it do this for IDE devices other than HD?! But let's leave this alone for the time being.
2. Get a Windows98 SE bootable floppy.
3. Log on to BIOS Setup Menu and make sure that the BIOS recognizes the CDRW properly.
4. As you will need to check both PIO and DMA mode support for the CDRW, choose one of the settings (working DMA is preferable, of course) in the BIOS. Later on you'll check the other one.
NOTE: On my older PC, there is no setting in the motherboard BIOS to specify PIO or DMA support (for the HDs, I used such settings on the add-on card BIOS). But I believe this is not your case with the new PC.
5. Boot into MS DOS with the CD-ROM support. If the drive can access (read) a data CD fine, you can proceed to the Win2000 boot.
NOTE: You do not specify whether you flashed the FW in the new or old (or another) PC. If you used the new PC, I'd expect the CDRW will pass the DOS Okay. If not, however, the problem is to be solved before it comes to the Windows.
6. Boot to the Windows Safe Mode.
7. Check via the Device Manager if the CDRW is properly recognized.
8. Disable AutoPlay and its Notification. I can't remember how it was under W2K but you always can open the Windows Help.
9. Insert a pressed (also, later on you can try a CDR) data CD in the drive. Open the Windows Explorer and check if the files are properly accessible (just readable).
10. Go to the Microsoft Configurator menu. To do it, open CMD window and issue command "msconfig".
NOTE: If the Service Pack update has misplaced the file MSCONFIG.exe, find it on the hard disk and copy on the search pass, say, to \%SystemRoot% directory.
11. From this menu, temporary disable any programs that automatically start at Windows boot. Later on, you can reenable those of them you agree to keep on a one at a time basis with checking for compatibility with your burning program(s) and other software at every next reboot. So, please keep tracks of your changes to this menu.
12. Exit the MSConfig menu and agree to restart the system.
13. Make sure that the Windows shutdown and consequent boot up go without any issues. If not, please never economize on system reboots!
14. Boot normally and first of all update the Nero to the latest version. Currently, it's 18.104.22.168b but you can wait a few days until the next one released. Also, it is a good idea to download the latest version 1.2.00 of the Nero InfoTool.exe. Keep, under another name, the imbedded in the Nero version 1.0.33 as it has some features omitted in the newer version.
15. Go to the Device Manager and make sure the DMA mode for your secondary IDE channel (i.e. CDRW drive) is enabled.
NOTE: If this mode proves to be inappropriate for you, it is the motherboard manufacturer (VIA Tech) bus master driver issue. You have no choice but to wait until they fix the problem. In the meanwhile you can stick to the PIO mode. It is some loss in performance but is affordable one, especially as it avoids any compatibily problems the VIA drivers are so famous for.
16. Exit the DevMan and restart the system. Make sure the shutdown, then boot are Okay. Recheck if the DMA mode is enabled and AutoInsertNotification is disabled. If not, fix it.
17. Invoke the "three-finger" Windows menu and check for any applications running.
18. If the Nero InCD is present, kill it forcefully.
19. Whether you can do the same with any other annoying program, it depends. But anyway notice any program present in this menu. On one by one basis, get into such program configuration menu and request not to start automatically with the Windows.
20. Go to MSConfig menu and prevent auto loading of any program you do not need for testing the CDRW drive. Exit and agree to restart.
21. Check again everything I've mentioned above. Proceed if Okay.
22. Only now can you talk about using the drive for writing (let's leave the re-writing alone: I don't care about it) in a considerably clean Windows environment.
23. Try to run the Nero and see what happens. If the problem still persists, switch to the PIO mode for the drive. If this fails too, you may start thinking about giving it. But not yet, of course!
Good luck. And please keep us informed.
P.S. Please bear in mind that every time you cut a corner in the somewhat lengthy but correct procedure, this causes an unnecessary post exchange and your still returning to the point where a bobby presented you with a ticket.