15 gigs is a pretty small partition, and if you designate 4 gigs for swap, you will have only 11 gigs for your install. Even if you cut your swap down to 2 gigs, and you manage to install in the remaining 13 gigs, you will run out of room to do anything in a very short time. I show a 64-bit 13.08 KDE installation (with no upgrades, and no additional packages), at close to 11 gigs.
How much room did you have on the "other machine"?
How big is your target drive? It is very strange that you would wipe it clean and still only have 15 gigs. How big is the windows drive, and did that drive come with the computer? Is it identified as sda?