@dribs,
Thanks for that info. That answers my questions 1-3, doesn't answer question 4 (regarding the "cannot write" problem that you mentioned), and isn't as detailed as I had hoped about question 5 (the step-by-step list of what you've done). It also doesn't answer the question about importance, so I'll assume the data is unimportant and not spend too long on my reply. If the data actually is important, please reply to that earlier question.
I'm worried about the "drive ... stop registering on laptop" comment that you made, but that's not enough detail for me to understand the exact sequence of events. I'm assuming that the drive was not physically damaged by this, but if you have knocked the drive, that assumption may not be true.
In short - this sounds like a WinXP full format, on what I guess is an NTFS formatted drive. The actual data blocks should be untouched; part of the filesystem metadata ($MFT) will have been overwritten making successful recovery of some files likely to be less likely; if there were many files on the drive (meaning $MFT is larger than the default) then some filesystem metadata may not have been overwritten by the format, making successful recovery of the files in that (unerased) part of the MFT more likely.
However without details on the "cannot write" problem as I asked, as well as more details of what happened leading up to that behaviour, I don't want to waste time making more comments at this point, as I don't have enough info to be sure I've understood those important details. Other readers might understand your comments better than me.
As I said before, do not (attempt to) write to that drive!
Edited to add: Ah, while I've been typing this, I see that I have interpreted your word "recover" differently from
pcimage, and I now see that this was ambiguous in your original posting.

If you actually mean that you want to (try to) "fix" the drive, and not "recover data", then of course my reply would be different. Please clarify...
@pcimage - Very good point. Damn, I hadn't realised that the word "recover" might have meant "fix", as you have spotted.