I have one computer with tws and my charting software only. I only use IE on this computer to access my IB account. I do not browse or do email on this computer. This is one of two computers that are hooked to a router with firewall. My question is: with this arrangement is there any way any kind of trojan or spyware can get on this computer?
Yes, from the other computer on your network which you presumably do more "risky" things on like general browsing and email.
I did not know that. This can happen even if they are not networked (softwarewise) and file sharing is not enabled?
No, not if they are not networked. I assumed since your first post said they were both plugged into a router that meant they were on the same network. Edit: After re-reading your edited post it sounds like they are on the same network. If so, disabling file sharing is good but its not everything as there are other ports that a Win PC will be listening on. You should run a software firewall on the trading PC as well so that there is no way for the other PC to infect it (block all ports).
Install something like zonealarm on both computers. Make sure that the other computer is treated by each as "unfriendly" (ie internet zone) which will cut your risks down. Then run spyware software every few days anyway.
I edited my post but was too late. They are networked on the router but I have not set up a network in XP.