I just re-read all the posts from the beginning and I think I understand a little bit better now.
A couple things, no, you won't be able to take your xbox hdd and hook it up to your pc. It has been formatted in an xbox specific manner (FATx or something like that), you're pc won't be able to read it.
However, it sounds like when you turn on your xbox it goes straight to the error screen. No flubber animation, no XBOX logo, no nothing. If that is the case then the problem isn't with your hdd, because the BIOS isn't even getting booted yet. The problem is with your BIOS. Given the alternative, that the problem is with your hdd and you don't have a backup of your c: partition, it is a much better scenario to have a faulty BIOS on your mod chip.
So here is my suggestion (please don't hold me accountable, it's only my suggestion):
First off, I'm not familiar with the cheap mod, is there some sort of disable switch on the chip itself, or someway to turn it off without taking it out? If so, turn it off, boot up the xbox see what happens and report your findings.
If not, then I would suggest taking the chip completely out, chances are, if it isn't mis-aligned and/or all the solder points look good and are accurate, then there is something wrong with the chip. (perhaps they don't call it a cheap mod for nuthin') After removing chip, boot up xbox, see what happens and report your findings.
If that doesn't work, then somehow your boot sequence on your southbridge chip got overwritten (not sure if that is possible without knowing what you are doing, as M$ disables the write feature so that can't happen).
My guess, however, is that once you take the chip out (or turn it off) it will boot up to your m$ dash. If that is the case you have two options: leave it alone, or buy a new mod chip like the xecuter 2.3 lite.
If after removing the chip (or turning it off) it doesn't boot up to the m$ dash, then, again, you have two options: sell the xbox for parts, buy a new mod chip like the xecuter 2.3 lite. If you choose the latter you won't be able to ever connect to xbox live, as you won't be able to boot the system with the chip off. But that should be the only real downfall.
Anyway, good luck, I hope this helps.
hal.