I've seen your problem way back in 2007. This is in relation or similar to CSCec00968.
Symptoms: PC with Intel 10/100/1000 NICs would "flap" when users have logged in. You might see comments something like "interface blah up/down N times per minute". When the users logs out, the interface will auto-negotiate to 10/Half and remain stable. Not all 3500 switch will have this issue. But I can't guarantee that the status quo will not change/deteriorate. This is not reliant on firmware: Win 2K, XP, Vista
Cause: The cause of this issue is the inability of the Intel NIC's and Cisco controller's to negotiate with jitter.
Workaround: There are two methods of workaround. 1. Hard-code/force the PC NIC and the switch port to 100/Full; or 2. Hard-code/force the PC NIC and switch port to 10/Full.
If you have further PC's coming from HP, you can request HP to provide you with Broadcom NIC. This will also help.
Understand that the 3500 series is End-of-Support so you'll have to understand why further IOS upgrade is no longer available. It is also this reason why Cisco/Intel/HP is un-willing to provide any patches to your particular issue because it just won't be financially justifiable.
If you contact HP or Intel for assistance, be prepared to be told that Cisco's got a "patch" for this issue.
