The first thing I would suggest you do is go to the site below which shows the minimum hardware requirements for Zorin. Compare that to your actual hardware to see that you meet the minimums. If you don't, you'll be wasting your time.
If reinstalling gives no disk space, you probably did a second install to another partition.
Zorin uses the Ubuntu installer and there is an option in the installer, at least if you select the manual/expert option which might be called 'Something Else', to format the partition. If you boot the Zorin DVD/flash drive and go to the Desktop, open a terminal from the Z menu and run the command: sudo fdisk -l(Lower Case Letter L in the command) and post the output here so people know what they are dealing with. It would also be useful if you could post some information on the hardware on your laptop.
There is also a link on the page above to their guide to installing. You might look at that and compare to what you saw during your installation.