Have you tried to partition the drive before attempting the install? When you boot the live CD, on that first desktop, go to mintMenu > Administration > Partition Editor. Make the partitions as you need them (/boot, /swap, /, and /home - for example). Once you have those set up and formatted, then click on the Mint Install icon on the desktop. When it comes to the partitioning step, you can manually set up the mount points in the partitions you have already assigned. Sometimes this method works better than just doing it in the installer. It might be worth a test.
The CPU and RAM seem much more than adequate, even more so than any machine I have running Mint 5! I am assuming this is a newer system with an older hard drive. Did you assemble this new rig with pieces from older systems? I do that often myself. Sometimes a look-see in the BIOS might be a good idea in case of boot order or PATA/SATA settings. I am tossing out some ideas, and probably items you have already checked.
What motherboard do you have? nVidia graphics, perhaps? I know Linux will install on a 15 GB hard drive. In fact, if you had maybe 128 MB for /boot, 512 MB for /swap, 6 GB for /root, that would still leave you with 8 GB thereabouts for /home. Anyway, post back with the results of the use of the partition editor. Good luck!
If anyone else has any ideas, feel free to share your suggestions.