Yes its true that I installed the OS first before trying to recover the data, but the XP OS only takes up 1 gig of space, therefore the undestroyed space that is "available" is still 19 Gigs, which still doesn't account for the data that I lost. Because as you said, the space is still there, "UNTIL you write information there."
And as you said, "It is very hard to recover data that has been written over." But only 1 gig of space has been 'written' over, as this is the size of the OS
--Captain Kirk
Again, you're assuming something, which makes you wrong.
For your assumption to work, all the data needs to be lined up neatly next to each other. Even a very defragmented drive will not all be contiguous. Parts of any individual file are spread all over the disk and various arrays on the disk 'memorise where these parts are' for later recovery.
By overwriting any of the disk (particularly the inner HDD tracks as happens on newly formated disk), you are destroying parts of these files, making the rest incomplete. Yes, the remaining 'parts' of your files will be on the other 19GB, but it is now garbled.
Essentially you completed what a proper format does, which is to write to the sectors. By installing the OS you almost couldn't have done more damage to your chances of getting the files back.
If it had've been a simple format, you'd probably have the data back by now. A simple Windows Recovery and Start up repair wouldve sorted it.
The only way to possible get back is if you have back up.
I would also complete a diskcheck.
Partition your drive so that if the OS goes pear-shaped, your files (on a secondary partition) will not be touched during reinstall.