We have a number of CAT3 runs that run 100Mbps just fine. CAT3 can support it if it was installed well (nearly to CAT5 standards - not untwisted over 1/2" at terminations, no sharp bends, etc.) The problem is that while one run may support 100Mbps, another one right next to it, even going to the same wall box, may not. So it can support it, maybe even reliably, but not necessarily predictibaly.
Follow the advice of the others. Put in a fiber backbone. The fiber itself can handle gigabit speeds, so if you don't have the budget now you can always upgrade trancievers later while using the same fiber. Ideally you should use 10/100 switches in your distribution closets connected to each other with gigabit fiber. That way you have the backbone speed to support multiple 100Mb pipes out of the switches. If you dont have the budget use older 10/100 switches or hubs as suggested with 100Mb fiber connections.
If your workstations have 10/100 cards and you have 10/100 switches/hubs in the closet, set everything to auto negotiate and connections that can support 100Mb will come up that way, while the other will come up at 10Mb. If you have a connection that comes up at 100Mb but has a lot of errors, force the NIC in the workstation to 10Mb.
Once everything is running again, you can redo the drops at your leisure. When you redo the drops, make sure you redo everything. CAT3 patch panels and wall jacks have to go as well as the wire. If you have raceway with sharp bends in it, that will have to go as well. Look at the cable manufacturers sites for info on wiring CAT5. True CAT5 performance doesn't just come from the wire, but the way it's terminated and how it's run as well.
Good luck.
Jeff
masterracker@hotmail.com
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