I once had Windows 98 on my origional computer, but now I am using XP on a laptop and, would like to still use a compressed zip disk. But, it was compressed with DriveSpace3. How can I use this compressed zip disk even though I am using XP and not 98?

Hi welcome to PCHF this is suposed to work.
go to www.bootdisk.com and download a win98 boot disk, or make a boot disk
which has 4 files: io.sys; msdos.sys; drvspace.bin; scandisk.exe. You will
also need to add a drvspace.ini file to the boot disk, sample below:

AutoMount=1
FirstDrive=D
LastDrive=E
MaxRemovableDrives=2
MaxFileFragments=101
ActivateDrive=D,E0

The above will load drive D: with the compressed info, and use drive E: as
the host. Adjust to suit your system.
You will need to boot the floppy after you have attached the hard drive to a
working computer. Once the OS loads, type scandisk /mount D: (or whatever
letter your compressed drive is in the computer). That will mount the
compressed disk and make the files accessible. Copy them to your new hard
drive.

You will lose the long file names but this is the quickest and easiest way
to access the data. Otherwise, install it in a working Win98 system.