Since simple plugging and unplugging has an effect, this is a job for a sniffer!
Put a sniffer (Ethereal) on the server that’s suffering, and plug the old server in and try your test.
I could guess at possible outcomes, but in this case, the actual answer should be easily found.
If you can’t detect anything odd on the server end, then put the Ethereal software on your test workstation and try again.
Write back and tell us what you find please.