"Happy, happy, joy, joy." :-)
Yes, I got the CD-RW working again.
For anyone that might be interested, here's what I did.
I looked at the MTKFLASH "how to" page that MediumRare suggested, but didn't see any really new info there on the basics for using MTKFLASH. The page recommended version 1.55 or, if that fails, 1.80.1. I d/l'ed both and tried them with some of the firmware files that Litefirm had extracted from the BenQ DOS firmware programs. Same problem. They would count to 100 % for banks 0, 1 and 2 and say that each of them was, in turn, OK, then count to 50 % of bank 3 and stop. I'd give them a couple minutes and nothing. The only difference I saw was that when 1.80.1 stopped at 50 %, it totally locked the computer and I had to reset. When 1.48 and 1.55 stopped, I could use Ctrl-Atl-Del to reboot (Ctrl-C didn't work).
MTKFLASH _was_ communicating with the CD-RW drive. Aside from the fact that it was apparently writing the first 3 banks with no problem, I could use MTKFLASH to read the firmware from the drive. The only IDE devices connected at that time were a hard drive and the CD-RW, so MTKFLASH wasn't talking to another CD drive. When I used the "C" (Check) option, MTKFLASH reported the following:
MTKFLASH By Joseph Lin (Ver 1.80.1)
ManuId : ad ManuId1 : 0 bDevId : b0
Flash Type : HYUNDAI(HY29F002T)
I noticed that when I compared the firmware file that MTKFLASH had just read from the "dead" CD-RW drive with the firmware file that I tried to flash, the files were the same until byte 38001 (hex). That is 7/8 of the 256 KB file, or 3.5 out of the 4 banks (assuming all 4 banks are the same size). That would seem to confirm that MTKFLASH was writing the first 3 banks and 50 % of the 4th.
I wasn't really sure what that told me, but it did suggest one possibility. The firmware version I was using before this was V.TW. Looking at the bad firmware file that MTKFLASH read from the "dead" CD-RW, at least some of the data in that last 1/8 was intact. I could still see the V.TW version number near the end, for example, which I knew was a leftover, because I had no V.TW firmware file to try to use with MTKFLASH. If the last 1/8 was intact (because MTKFLASH and ArtecDHM.exe, which was really MTKFLASH v1.48, had never overwritten it) and I could use MTKFLASH to flash version V.TW, then the fact that it couldn't/wouldn't write the last 1/2 of bank 4 might not be a problem, since that part may already (or still) be there. But I didn't have a V.TW firmware file. The only BenQ V.TW firmware I've found is the Windows program, and Litefirm doesn't see the firmware in that file (it only worked on the DOS versions of some older BenQ firmware programs).
So then I decided to see if I could extract the firmware from VTW.EXE myself. I hadn't considered trying that before because I had just assumed that it wouldn't be that easy to do, but it was actually quite simple (given the proper experience and tools). I've been working with computers for over 20 years, mostly running Unix. In that time I've looked at countless "binary" files looking for data of one sort or another.
I looked at the firmware files that Litefirm had extracted from the DOS firmware programs, found a distinctive string near the beginning of each one, found that string in VTW.EXE, backtracked from there to the likely start of the firmware data and extracted 256 KB of data from VTW.EXE, starting at that point. Finding and extracting the data probably took around 5 - 10 minutes. Then I used MTKFLASH to flash that firmware file to the CD-RW.
The first time I tried was with MTKFLASH version 1.48 (or maybe 1.55) and I got errors. I don't know if the problem was me (bad command options) or the program. I _thought_ I entered the command correctly, but maybe not. So then I used version 1.80.1 and it ran as before, counting to 100 % for banks 0, 1 and 2 and then stopping at 50 % in bank 3. I gave it a minute or two and hit reset. Sweaty moment as the CD-RW still didn't seem to be responding, but then I turned off the computer and when I powered it back on, the LED came on. The BIOS saw the drive, no problem. I booted Windows, which also saw the drive, and ran BenQ's VTW.EXE to make sure the firmware was correctly flashed. VTW.EXE saw the drive and reported no problems flashing it.
I can look at the contents of a CD-ROM and burned a few files to a CD-RW disk with no problem. Another small sweaty moment when Nero's InfoTool said that the maximum write speed was 4X and read speed was 30X, instead of 40X and 48X. But, as I had hoped, that was because of the CD-RW disk I had in the CD-RW drive at the time. With a CD data disk or CD-R, they went back to 40X and 48X.
I've got the DVD-ROM and CD-RW back in place as secondary master and slave and both seem to be working fine now. Gee, what fun. :-)
So, the key, at least for me, seems to have been that the versions of MTKFLASH that I've tried can't, or won't, write the last 50 % of bank 3 (the 4th bank). That meant that that part of the original firmware was not changed, and could not be changed, by MTKFLASH, so I had to use MTKFLASH to reflash the first 3.5 banks with the firmware that matched the last 50 % of the 4th bank.
I'd be happy to email any of these extracted BenQ firmware files to anyone that's interested, but I don't know if they should be just posted on a Web site, since, based on my experience, trying to use MTKFLASH to flash anything but the firmware version that you were already using won't work. Posting the firmware files on a Web site without an explanation is just asking for trouble. Also, for the record, I have no way of knowing if most of these firmware files are actually good. It's a pretty good bet that the V.TW file is good, since that one got my drive working again (because that was the version that the CD-RW was using before this started). AFAIK, the other firmware files are fine, but I don't have any proof of that. I could try flashing with a BenQ firmware program (eg. VMW.EXE) and then use MTKFLASH with the corresponding firmware file (eg. vmw.bin) and see if the drive still works, but I'm not that dedicated. :-)