BMM389EC,
Networks aren't too bad, you just need to be methodical so that you can pinpoint where the problem lieth!
I assume that you are cabling both PCs to the Linksys switch ports, and that the Linksys is configured to supply IP addresses to each PC via DHCP, and is in turn connected to the broadband device.
You can view the IP configuration by typing IPCONFIG /ALL at the command prompt (Start, Run, CMD). Check that both computers have an address in the same range (e.g. 192.168.0.2, 192.168.0.3) and that the Subnet masks are the same (e.g. 255.255.255.0). You should also ensure that they both have the same Default Gateway (the Linksys device, probably) and are both picking up the same DNS servers.
Check that each PC can communicate with the Default Gateway by pinging it from the command line: PING 192.168.0.1, or what ever the DG IP address is on your network. Next ensure that each computer can ping the other: PING 192.168.0.2, or what ever the addresses are on your network. Then check that you can ping the NAME of each computer from the other: PING MYPC1, or whatever (to find the name, right click "My Computer, Properties, Computer Name Tab).
If you can do all this, then the problem lies further up the chain, and we can investigate shares and security issues.
If you can't, report back so that further troubleshooting can be attempted!
SD