Let me start by saying that this sounds tricky.
It would be helpful to know what software created the backups. Without knowing that, you are working in the dark, and so some blind experimentation may be needed.
If these files are of any real importance, your first step is to make sure you have suitable backups. Otherwise, whatever program you use to restore files might change the files. Also, it wasn't clear how you're using the floppies: if the data is on floppies, or if you were just using them as part of a restore technique. Floppy disks can deteriorate with age and usage, so get at least one copy of the data onto modern hardware. And, if you really care about the data, make another copy of the data (which should be easier after at least one copy is on non-floppies).
Software like DOSBox might use standards, like 1.44MB disk formats in disk images. However, actual backup software from that era would sometimes do things in ways that were not quite so standard, like fit 1.76MB on a floppy. So I would suspect that using software like DOSBox might cause restoration software to not work as expected. DOSBox gets lots of reviews for being great, but it can't handle data right if it doesn't see a copy of the data. To maximize the chances that you have every critical "bit" of data, it might be necessary to create disk images of any floppies.
I've heard that the Backup and Restore programs built into DOS are specific to the version of DOS being used. So you might need the restore program from the same version of DOS, if that is how they were backed up. Even worse, I have heard that such programs were buggy.
What you are missing might be the first file in a series. Some programs would start numbering, starting with the second archive file that was created. For instance, ARJ files would use file extensions of ARJ, A01, A02, A03, etc. RAR files would use file extensions of RAR, R01, R02, R03, etc. (Actually, RAR had another pattern of some sort as well, depending on the version of RAR being used.) As for a program that just used pure numbers, I don't readily recall one, but I do think that too many programs used the pattern of just naming files after numbers, so that is not a telltale sign that can let someone just easily point to one specific program. Any specific advice may be a long shot that is more likely to be wrong than right. I realize this wasn't intentional, but the question ends up being fairly broad just because there are multiple possible answers.
Providing further details in an answer is probably infeasible without more details. Knowing the characters of the archive files may be much more helpful for humans to figure out the file type. There may be a pretty decent probability that even just the first 3 to 5 characters might be sufficient to give some key clues, while being rather low in likelihood of sharing damaging data. To figure out those bytes, you would want to view the files in a hex editor. That actually stands a good chance of providing some substantial clues on how to open the files. You might want to get permission to share the files-- if not to the whole Internet, then perhaps with a rather trustworthy expert who is bound by an NDA.
You mention that utilities are asking for a drive letter. It could be helpful to know just what those utilities are. Most of the more useful programs I've used to interact with archive files would typically take a filename. So, knowing what software you suspect may be helpful for people to agree, or rule out some ideas.
Since it seems you're desiring drive letters, make sure you know about mounting directories to drive letters. In DOS, SUBST can do that. In Windows, SUBST might also work there. Also, SMB file sharing can do that (by mounting a shared folder... this can be done using NET USE from the command line). In theory, APPEND or JOIN might also do similar things, but in actuality what I've read over the years is that those programs are probably more trouble/danger than help, so you probably want to stay away from those. (Things like operating system bugs, or differences between versions, may make them more of a liability than a positive use.)
I wouldn't put much faith in the TrIDNET analysis. I'm not familiar with the program, and so it might do a fabulous job. However, the answer that it is an old Norton file just seems like an answer that might be based on guesswork.
I know I threw a lot of advice your way. If you were looking for an actual clear-cut answer, it was the part about using the Restore program from the right version of DOS. But, I do admit that although the answer might be technically correct, it may admittedly have a somewhat low chance of success if you don't know what software that was.
You sound like you might just be looking for advice/direction/any-hints at this point. Well, in my opinion, the most promising approach is probably to look at the hex bytes and get a better idea of what types of files you're working with. Then you'll at least be in a far more informed position to ask some more specific questions.
Get HDD Hex Editor Neo (free) to examine the files and see the headers. If the first 2 letters in each file are "PK" then they're zip file, so get 7-Zip (free) to unpack the files. I suspect once they're unpacked (if they're zip files) they're individual files from the file system, only larger files were "split" so the parts would fit on a single diskette, so you will have to figure out how to put the pieces together. If they're not zip files you can still use the hex editor to examine them and see what you can find. (zip format: http://www.pkware.com/documents/casestudies/APPNOTE.TXT .)
– Daniel R Hicks – 2014-08-11T00:32:54.0501The extensions indicate that the files are a set of backup or compressed data stored to several diskettes (since the data would not fit on 1 diskette). They were either created with a backup program or with a file compression utility. The best way to restore them is to determine the program that created them (as Daniel R Hicks stated by looking at the first 2 (40 would be better) characters in the first file). When you run the restore program, it will probably ask for the last disk (to get the index). – LDC3 – 2014-08-11T00:52:18.077
1Well, this is a perfect example of how obsolescence can be harmful in unexpected ways long into the future. – That Brazilian Guy – 2014-08-11T00:57:00.567
Are each of those
.00x
files 1.44 MB in size? If so, it means each file represents a floppy disk. What is the filedate of the set? It can help in knowing the date it was created and possible software versions popular at that time. – That Brazilian Guy – 2014-08-11T01:23:48.340http://www.willsworks.net/dosbkup.htm may be of interest. Looks like there were at least two versions of norton backup 1E and 2A so your version of norton backup is probably too new. Norton backup on dos seems to be versions - the software linked there seems plausible but there's no way to test it. – Journeyman Geek – 2014-08-11T02:03:45.393
I've already attempted to open the resulting file with WinZip and 7-zip. The 001 through 009 thing isn't the problem, it's that the resulting file is unretrievable in its current state.
I've tried quite a few versions of Norton's DOS backup utilities (I found a package of Norton 5, 6, 7, 8, c5, and CO(?). The issue isn't that I have wrong versions (I think)... it has to do with the way the programs read the files off of the disks. Is there some other method to pack the individual parts onto floppies so it actually tries to open them? Right now it just says there's nothing there, and stops. – user2085722 – 2014-08-11T02:29:18.157