I'd like to know how to go about installing linux on a computer with no monitor or CD drive, but has a floppy drive. It is connected to my network, of course. I'm aware that PXE would allow me to network boot, but I'd like to do it non-PXE (assuming I would have the computer boot a floppy), mainly because I don't want to set up a DHCP server.

So, I know what I want to do, the problem is exactly how to do it. I have a copy of Mandrake 10, but I can download another distro if it would do better. I'm not currently running any linux distro - just Windows XP. How do I make a boot floppy to make the remote computer search for the installation over the network, and how would I set up my local computer to put out the installation?

Welcome to LQ! This procedure is called headless install. Serial port is used for user input (serial console). Try googling for 'headless install', should bring up something.