You say it didn't work, but you don't say what happened when you tried it? And you don't say what services you're trying use with these connected servers?
I'm going to assume you just want all of them to access the outside internet? And that there are, say, 12 machines? And that the rooms are less than 25m apart?
The easiest way, if you want a wired LAN, would be to buy a basic router like those from linksys or netgear. Buy one that has 16 slots (more than the 12 machines assumed above) so you don't need 4 switches. Follow the 1-page instructions in the router to plug the router into your internet connection, and run cables to the rooms with the computers.
You can buy 25m CAT5e or CAT6 cables (with male plugs on both ends) and run them through the walls or along the baseboards. Plug them into your computers on one end, and the router on the other, and voila.
(It would be prettier to run them through the walls and put jacks in the walls, but that requires carpentry skills, and is more error prone from a networking perspective.)
The legal distance for cables is, I believe, 100m. In practice (with professionally made cables) you can get longer than that. So I doubt distance is your issue unless you're building cables yourself.