It looks like this is one of those times where you just have to accept the uncomfortable reality that your hardware is most likely dead.
All electronic gear can die suddenly - particularly anything that has moving parts such as drives. Over the years, I've had relatively good luck with drives, but across all my computers I've still had to toss a floppy drive, two CD-ROMs (one back in the days when a CD-ROM was expensive) and a couple of hard disks. I also had to RMA a bad string of tape drives, but eventually got a working drive whilst I still had a warranty (just as well - these drives cost over US$1000).
I've had better luck with other hardware - obviously keyboards and mice wear out, also I've had a couple of CRT monitors fail (transformer burn-out in both cases, most likely - and not worth sending for repair as the bench charge would have been over half the cost of a new replacement). My old Pentium 133 machine only died last month (seemingly from power supply failure).
My real expense, though, has been in dead scanners - I need a high end scanner for various reasons, and none of mine seem to last that long. In fact, I'm about to complain to HP that my 11 month old ScanJet 7450C is not working properly - I want some kind of resolution before the warranty has run out. Along with their cousins, optical drives, the repair options for scanners tend to be very limited, not least because they can be a pain to set up again once disturbed. HP won't service scanners at all - outside warranty they just offer an exchange which is so expensive you may as well buy a new one.
The only comfort is that usually you can get something that performs much better than your dead hardware for the same money - or even less money than you paid for the original.
It sounds like you've done everything reasonable to try to test the drive - particularly trying it in another machine. Reflashing the firmware - worth a go, but I'd be very surprised if a flash memory suddenly blanked.
You may be able to find some more information on diagnosing the drive, but realistically it's unlikely to be repairable even if you can diagnose the fault (most computer hardware is only ever reworked for a handful of standard faults - beyond that the bench time for repair is so expensive that it's cheaper to toss the faulty item, which is why warranty replacements are sometimes new). The only possibility that's a little more comforting than it being completely dead is that it still works on DVD media only.
I know you feel you haven't used the drive much - but power on hours is one determinant of when drives fail, through factors such as heat and dust build-up. Assuming there's no warranty left and nobody comes up with any specific advice as to a repair attempt, then, as a last ditch attempt, you could try opening up the drive and gently blowing out the innards in case the problem is dust. If there's nothing else left to try, it might be worth a go. You may also see something stupid with the drive's cover removed - a belt that's broken, a spring that's come off - something like that. Don't be tempted to power up a drive with the casing removed, though - there's quite a powerful invisible laser inside.
The reality of the situation is that a new DVR-107, or, if you can find one on close-out, a DVR-106, or possibly another manufacturer's drive (like the excellent NEC ND-2500A I have) is your only way ahead. You'll land up paying much less than you did for your probably dead DVR-104 for a much faster and more advanced drive.