Okay -- so DiskWarrior ties up your computer for 2 weeks while it does it's thing?
If your hard drive directory is disastrously scrambled, DW can take days to sort things out, but in 95%-99% of all cases it takes oonly a few minutes. Norton Disk Doctor is perfectly capable of scrambling it disastrously, but if your Mac still starts up and runs, things probably aren't that bad yet.
A damaged directory makes it likely that there will be some loss of data if you simply copy the entire drive to a backup disk now. The bad directory means the OS can't properly locate every file that it knows is supposed to be on your hard drive, so some of them aren't going to be copied properly. It might be just one insignificant file, or dozens or hundreds of important ones, that are damaged in part or lost altogether in backing up. The ideal time to back up your drive is when you know it's all in good order.
Erasing your hard drive will also erase the bad directory, so it's an alternative solution to the problem if your data is already backed up. Copying the contents of a backup that you make now, with a damaged directory, back onto your internal drive after erasing it won't fix any files that have already been corrupted, but it will at least copy everything — damaged or not — back into a new, undamaged directory.