I'd guess ethernet autonegotiation problems. Are they managed switches? Can you force them to 100Mbps/full-duplex?
I inherited this network setup, and it's essentially a larger home network, so no, they're mostly using little Linksys switches.
I really can't swap switch #1 with anything because it's back in the server rack we just set up when they added on to the building. Essentially the hub of the network moved into this new construction, and an underground Cat6 cable (I think they put in Cat6 and not Cat5e) feeds a switch in a maintenance closet (switch #2). That switch in turn goes up to an office where the cable modem and a router used to sit before it was moved into the new construction. Because it wasn't approved to run new drops to the offices, I basically swapped out the modem and router for a switch.
This was all working just fine until a week ago!
Perhaps you have a loopback between one or more switches and the network is saturated?
Is there a way I'd diagnose that?
Did disconnect the computers connected to switch #2 and #3? It could be something running on multiple computers, bad network cards, a bad switch or bad cables.
I did try disconnecting everything but switch #2 and plugged my laptop into it, and got slowness. I also tried the same but replaced switch #2 with a completely different switch, and I still got slowness. But that was an older switch, so I'm going to try a new one today.
By the way, I gather that the effective length of Cat5e is 100 meters, but isn't it boosted again if a switch is placed at the end of it? Do I get another 100 meters? Or is it lessened significantly? I'm not positive of the distance between #1 and #2, but I know it's not more than 100 meters.