Won't Install Permanently or Reboot

After installing 9.10 on my HP desktop PC - booting from ISO image on CD, it seems to install a temporary version which seems to work okay. The "filesystem" is only 181MB free, so it must still be the temp/trial version as it has an 80GB drive.
There is an icon on the desktop which says "Install Ubuntu 9.10" with mouse over help stating "Install Ubuntu Permanently..etc".
If I click this icon, it takes me through the same installation process and I am back to square one.
If I reboot, it just hangs, or says it can't find CD, etc. - or sits there with a black screen with cursor hanging in the top left corner.
IT will only reboot from the CD again.
When going through the installation process again and I get to the partition step, you can see that it says Ubuntu 9.10 install on whole disc already.
It doesn't seem to install permanently on the PC and be able to reboot on it's own without the CD and have the full 80GB free on the filesystem?