"Tbragsda" has it right. Don't go off half-cocked or you will be chasing ghosts through the LAN. Calm down and take a look at what EXACTLY you are having issues with. "The Network" means different things to users than to IT staff.
What is being seen as slow? Moving files? Copying data? DB access? Login? What happens when people are gone? Does it happen only at a certain time? Have you tried turning ALL systems off, and bringing them up one at a time? Have you put a sniffer on the wire to examine packets? If you are unaware of how to troubleshoot the LAN, call in someone that can, and insist on "knowledge transfer". We all started from the same place. Zero knowledge.
I inherited a network a few years back that had an issue every morning and every afternoon. The network would slow to a crawl. Less than 2Mbs throughput, lost packets, all manner of trouble. I spent several days examining the traffic and looking at cables, NICs and such. Turns out that an improperlyshielded cable was run through the wall next to a really old photocopier. When the copier was turned on and used, it caused crosstalk. I noticed that the receptionist's routine of copying for everyone in the office occurred at the same times as the outages. I moved the copier and was a hero for a day and a half.
Another result of this exercise was finding several older network interface cards (NICs) that were "jabbering". They were failing, and as a result, outputting garbage packets on the wire. Replacing them increased the speed of the network immensely.
In the long run, you WILL want to go to a switched environment, but do it with forethought, planning and good reason. Not as a knee jerk reaction to an unexplained error condition. Your credibility is at stake if you don't find and correct the error.