Did you install all of the software on the included disc? If so, remove Sonic DLA, and keep RecordNow. Likewise remove Nero's InCD and Roxio's DirectCD if present.
Zip to the store and purchase practically any other brand of DVD+r discs. I noticed that you are using TY. They are often faked.
Update or removal of 3rd party IDE drivers? (don't remove your SATA drivers!)
Viruses? Or virus scanner operating during dvd writing?
Can you burn a CDR?
Consider Abit's adaptor to convert IDE drives to SATA?
With an entirely SATA system, your computer would perform better if you disabled the IDE system entirely (using bios options--see manual). It is possible to run both the hard drive and the BenQ on SATA.
Switch BenQ's jumper to CS (shouldn't work, but sometimes it does)?
Motherboard BIOS options and motherboard manufacturer's support forum? See if other users of this particular motherboard report trouble with the combination of SATA hard drive and IDE optical drive. I remember reading some little setting in BIOS options. I think it was Boot Priority or boot order--setting the optical drive either first or last. This also has the (normal) requirement of the IDE channel in use being set to AUTO detect and AUTO type (motherboard bios menus, standard options screen).
Consider using bios P9 until testing is completed.
Try RecordNow or the combination of DVDShrink+DVDDecryptor for burning as you may have a software-only issue.