DMA has nothing to do with the tray opening and closing, but should be enabled in any case.
This is the opposite to what normally happens if you leave the tray open when shutting down - the tray should automatically close during the sequence.
It's not clear from your thread whether you do have a rewriter as well. If so, do you have Nero by any chance?
This software controls the operation of the CD/DVD-ROM drive and/or rewriter and just might be the source of the problem. But it's only a guess.
It might also be worth deleting the CD-ROM drive from the system and letting Windows reinstall it at boot up.
You don't need a driver as Windows has its own generic version.