Huge boo boo with 10.5.7. Please help!

Were you using Time Machine, or did you have any other backup?

Firstly, I have read your other discussion about the "igetter". Nerowolfe raised the question as to why you did not use the normal software update, and I think therein lies a clue: A normally functioning system would give you the software update and after restarting twice, you'd updated from 10.5.6 to 10.5.7. That is something that could impossibly go unnoticed (your other post seemed somewhat surprised that you were already running 10.5.7).
Unless someone else had been tinkering with your system beforehand.

Secondly, more to your current problem, have you tried a startup while pressing the option key (it should give you the icons of available OS's to boot up from). Also, you could try and booting from the original Leopard install disk, run disk permissions from there, and on reboot, hopefully 10.5.7 appears, run disk permissions again from the OS itself.
If you get that far, you should go to system preferences/software updates/installed updates. That should tell you what you installed and when.

If you installed the software-update DELTA (the smaller one ±452mB) you might want to consider installing the COMBO (via standalone installer) http://support.apple.com/downloads/MacOS_X_10_5_7_ComboUpdate

Good luck

Your system may be badly hosed now and need to be reinstalled.

First get an external drive to make a backup. Beg or borrow the money to buy one if you need to. Hook it up to your Mac. Boot up from your Leopard DVD. Launch Disk Utility from the Utilities menu. Click the Restore tab. Drag your internal drive to the Source box, and your new external drive to the Destination box. Click the Restore button. This will back up your whole hard drive to the external.

When that is done, and while still booted from the DVD, use Disk Utility to Repair Disk. If it results in any errors being reported, run it again. Once no errors are reported, proceed with an Archive & Install. This will preserve your applications, user settings, preferences, etc.

If Disk Utility reports errors it cannot fix, you will need to proceed with an Erase & Install. After that you will have to recover your applications and user data from your backup.

Once you are all done with that, erase your external hard drive and use it with Time Machine. It will save your bacon if this kind of thing happens again.

DiskWarrior ($100) might be able to repair the damaged filesystem.

Before spending money on that though, I'd do a fresh install of Leopard on your new external drive, and then boot up from it. See if your damaged internal drive will mount on the desktop. If so, grab your data from it and put it in the corresponding locations on your new external OS X drive. Set up your new external drive just as if you intend to run permanently from it. Then you can erase and reformat your internal drive, and use a cloning utility to copy your external drive to your internal drive. You can then boot up and run normally from your internal drive, and you have the external as a backup.

" Unmounted" indicates that the computer will not accept the drive partition which is possible if the "volume header" is corrupt or no valid file system/ structure is found; in essence, it's like a library in Fort Know: you know the books are there, you can see the building, but you cannot get in because you either lost the keys or that the doors are locked.
The only way to try is to start your Mac from the OSX disk itself and try and run fsck , failing that "repair disk", and "repair disk permissions" http://support.apple.com/kb/TS1417
and see if that resolves it.

The fact that your machine names the volume " disk0s3" indicates that the information about that volume is either lost or not accessible.

Any good?