Where did you purchase the disc from?
How large is your hard drive and how much hard drive space do you have left?
Disconnect all peripherals from your computer.
Boot from your install disc & run Repair Disk from the utility menu. To use the Install Mac OS X disc, insert the disc, and restart your computer while holding down the C key as it starts up.
Select your language.
Once on the desktop, select Utility in the menu bar.
Select Disk Utility.
Select the disk or volume in the list of disks and volumes, and then click First Aid.
Click Repair Disk.
Restart your computer when done.
Repair permissions after you reach the desktop-http://support.apple.com/kb/HT2963 and restart your computer. Try upgrading again. Repair permissions and restart your computer again and post the results.
If you have a PPC G5 iMac (non-intel), Snow Leopard is incompatible with your computer. If you have an Intel iMac, it's possible your disc is damaged. You should call Apple Sales for another disc.