Are you sure that your DNS requests are being serviced properly? Perhaps steam operates on static IP's for their content servers or whatever, and anything relying on a nameserver lookup is failing.
Are you pointing your broken PC's DNS queries to the router, or to your ISP's DNS servers? I'm thinking maybe your wireless PC's are set up to acquire the network addresses via DHCP (including DNS, so they get the ISP DNS servers), while your static one was set up with a manual static IP, etc... (and so possibly are set up to send DNS requests to the default gateway - this sometimes behaves oddly, you should be able to rectify it with a router reboot).
- Dag