When I boot up I hold "Alt" and it brings me to a screen that says "Macintosh HD" and "MAC OS X Install Disc One" and "Hardware Test." . . . . If I slsect Install Disc One, I choose to install it without erasing my HD and I get an error message.
(1) That sounds promising-- If you can get to the Installer CD/DVD at all, then that means you can also get to Disk Utility on the CD/DVD, and can try the repairs that jsw and gnasher729 suggested above. If your C key won't let you boot to the disk (odd!), then at least this gets you to the same place. Different path, same destination.
When you get to the Installer menu (where you tried to install before), this time, you should instead go to the drop-down menu on the top left and choose Disk Utility. I am not sure which exact menu, as I am not on a Mac now. (Everybody, please forgive me.)
In Disk Utility, it should give you a list of disks on the left (your Installer boot CD/DVD, your hard drive, etc.) and a panel on the right. Select your hard drive if you can-- you may have to select the one just under it (i.e. if you can't select the hard drive itself, there is often a volume or something right below it that you can select.) For example, the top one might say MAXTOR 40GB and under that, Marty's HD, and you can only repair Marty's HD.
Once it lets you select something, over on the right, click on "First Aid". From, there, there are buttons at the bottom for [Repair Disk Permissions] and [Repair Volume]. Somebody can chime in for this, but in this situation I would click on [Repair Volume] first, then try to [Repair Permissions.] I even try it a couple of times; not sure if that makes it better, I just do it a few times on principle.
After that, try booting again. The next step might be booting in Safe Mode, but I may have to go look that up. Back in a bit.
If my hard drive is kaput anyway though, I don't think there'd be a chance of recovering my files anyway (although when I chose install Mac OS X Disc One it showed my hard drive as having 48.3 gigs free, which is the space I have left. If it was trashed, wouldn't it not recognize it?)
(2) I also have to recommend DiskWarrior. I, too, flinched a little when buying it, but it brought back a (non-visible) hard drive when I had a corruption problem. I can't guarantee it will work for you, but for me, the hard drive itself was fine; it was just a severely corrupted directory that wasn't even "visible" to the Mac, but DiskWarrior was able to rebuild it.
And, as you said, if your hard drive is passing the hardware diagnostics but won't boot up, then it is probably some sort of corruption and I would only wipe it as an absolutely last resort.
As a separate comment:
I must be doing something wrong, as the c key has yet to work for me. I'll try again when I get home.
As you have found, holding down Alt (or as you might often see it written, Option) calls up a boot menu, and you can select what you want to boot from there. The fact that it won't boot to CD with the C key but will with the Option/Alt key is really more than a little weird...it obviously sees the CD/DVD boot disk; I don't know why it is not paying attention when you use C.....
P.S. The hard drive in my signature is not the one I repaired with DiskWarror-- I think I bent the cable for that one. The Diskwarrior-repaired drive is still OK.