Nick,

This may or may not be related but I too have three PC's running on a Linksys router, I have had plenty problems with it in the past few months, sometimes connecting. sometimes not. After lots of research and going through it painfully slowly but logically there were a few things which could cause the problem, systematically going through them eventually got me up and running without any further glitches (which keeps the wife very happy now). Below are some of the less obvious connectivity problems:

1. if you use a wird connection, try setting the network card to 10Mb/s duplex cuz linksys have a problem with auto detect speed which bombs out the router. If you are using WIFI to connect, what happens to the conection if you can connect via direct cable connection (LAN)?
2. Try turning off UPNP in the router (not at the PCs) as the PCs are probably telling the router to reconfig settings independantly (effectively competing for connections).
3. As an experiment, try turning off WIFI security in the router and ONLY turning on the suspect laptop, if the laptop can "see" but not connect, the WIFI then it's probably the connection order which is suspect (you mentioned it connects to the office WIFI). Incidentally, at the office do you connect to a domain? Is your laptop on a static IP or DHCP? If it's static it may be tied to the office network, if its dynamic, then your router may not be issuing an address.
4. I've never been a big fan of Norton, but the latest release of Norton 360 is actually a very, very good product, and one of the nifty tools is a simple wifi and network scanner which shows all of the components on your home network, try the trial to check your network settings. Try the trial download to inspect the network, more importantly, the network settings.

Hope this may help