I had a case like that on my laptop computer, which even though a bit faster, doesn't have a floppy, CD, nor usb-boot option.
I installed Debian on my hard-disk by making a new like 50mb partition just for the Debian installation disk (network installation), booted from there (had to install grub first), and deleted the other partition (with windows on it) installing linux without problem. I actually used one disk I think with my removable CD drive because my net connection wasn't that fast back then and installed the basic packages just fine.
I didn't have another computer as you do, so I think it should be easier for you. You might just put that hdd-install disk (not the hdd-install by network one like me, the whole one or the 1st disk only), and maybe boot grub by a floppy. After the "base" install is done, you can mount iso images and use the package manager to get everything from there.
There are some reference/instrucions on the Debian website;
http://www.us.debian.org/releases/st...h04s04.html.en <- maybe this one, and you may also want to see
http://renaud.waldura.org/unix/linux-tp560.html