LinuxQuestions.org - Network Booting Question

I tried doing a search for this, but I am really unsure of what to call it. I know it can be done, I've seen similar setups before.

Ok, here's the setup:

I have a server pc running Debian Sarge 3.1r0a. It has an 80gb ata hard drive and a 18 gb scsi hard drive. it has a 550 mHz cpu, and 1024 mb sd ram. No graphical interface is currently installed, its just a bare debian system running NFS, Apache2, MySQL4.1, and a few other small servers including my own full debian sarge repository including security updates (this updates everyday at 4am). I currently have over 50 gb free space on the drive.

I have a computer for my kids in their room. I cannot install a linux OS on their system; for some reason every install locks up. Debian locks up right before hardware detection. Knoppix has kernel panic right when it starts booting. Mandrake will install after a few hours, but locks up during boot up. I recently gave up and just put Winblows XP SP2 on it. Install went smooth, and it boots up smoothly. It's slow, but it works. This system is a 233 mHz Pentium II cpu, 512 mb sd ram, 2 13 gb ata hard drives.

I really want to get debian on for the kids, and they want it too. They love linux over winblows. I remembered back when I saw a few networks setup to have one main server and the other machines booted off this server. The main place I saw this was at the public library.

I dont really know how they did it, or what its called, but I do know enough to explain it.

The server had an OS on it. The client computers didn't even have a hard drive let alone an OS. The client computers when turned on would boot through the BIOS then instead of checking for an OS on the HD, they checked for an OS from the server via ethernet. Once found, the client machine would boot up the OS on the client machine using files from the server.

This is pretty much what I am wanting to do for my kids. I want my kids' computer to boot up Debian using files from my server. Then they will have access to their computer's local drives. The bootup will look just as normal and wont seem like its booting from the network.

Here is a clarification: I dont want the client to actually boot up my server, the server is already going to be up and running 24/7. I dont want an SSH or VNC conection to the server from the client. I want the client to be totally independant of the server once it is booted up. The client will just use the server to actually do the booting up.

Does anyone know what I am talking about? I may be completely wrong about how this is done or how it works... Any clarifications or suggestions are greatly appreciated. If there is something similar to what I want, or even completely different please let me know.

When responding, please assume I am a total beginner at this sort of thing and spell things out for me if you can.

Thanks you very much in advance to everyone that helps me. :)