Unfortunately 16 over rides most other codes so it's hard to say for sure whether the issue is just some file corruption (error 13 or 21 for eg) or a more serious error 07 (dead drive). When a completely unmodded console goes to 16, as you say, it usually points to a hardware fault of some sort, but that said, there have been times when I've seen X-Boxes wipe files for no good reason.
First off, how easy is it for you to get the console booting off one of those other drives? Say you do that, you can then set the time; plug the "dead" drive back in, and you should get a more instructive error code.
If that's more trouble then it's worth, plug the drive into your PC like any other and boot up. Does the system at least recognise the thing is there? If so, then that's a good sign; sure, it'll probably be locked so you can't get a good look at it, but if the computer will boot and spot the drive then you can at least say it's doing something.
Next up, take a read through
this thread, paying close attention to
this post here in particular. Reckon it applies to you? Then let us know what brand the drive is and we'll try something along those lines.
If you don't have a Seagate or a Western Digital drive on your hands (and if you don't, please say what it is, I'm starting to suspect there ARE no other models out there), you may have to hotswap or build an EEPROM reader to unlock the drive.