Thanks for the extra info.
What version of Unix are you running, and on what platform? Knowing this, we may be able to advise on how to get the system in to at least admin mode to allow you to correct the problem. (As you're using diskedit.exe to view the disk, I'm guessing it's an Intel based Unix - SCO or Linux maybe?)
Also, could you post the exact messages you are seeing? This might give clues as to what the cause of the problem is. As the systems seems to get as far as trying to boot, it could be one of a few things that are wrong. Kernel may be corrupted, device file may be missing from /dev, etc.
Taking a flyer on one possible solution, if it is an Intel box you're running on then you may be able to use one of the many Linux-on-a-floppy "distributions" to get the system booted. From there, you *may* be able to mount the partitions you need the data from and back them off to tape, floppy, whatever. I say *may* because, without knowing what version of Unix you are running, there's no guarantee the Linux-on-a-floppy you choose will understand the file system you want to mount. ie, no drivers for a SCO vxfs file system, for example. (As an aside, I'm not even sure if there are drivers under Linux for SCO vxfs fs...)
Start at http://www.toms.net/rb/
for Toms Root and Boot. It also has links to may other LOAF distributions.
Hope this helps, a little.