This is how I run my server that I've recently set up. I use an old Dell Optiplex 210L Desktop with P4, 2GB ram and 160GB hard drive and it works fine. I run a little Minecraft Lan server on it and use it to share files and media streaming. I may upgrade the hard drive to a 500GB or 640GB. Anyway like Ssc said a machine like that will do the trick.
About your laptop if you can't remote into it then pull the hard drive and out plug it into a desktop.
Awesome,
Thanks for the input BK!
This is great. Now I'm just waiting till my spring break to actually start building my server and see if my dell PC can handle it. Hopefully I can get it to work.
By any chance you know what kind of windows server program I can use? I recently just got Windows home server 2012, i think, but its on my flash drive.