Let's get back to the wired connection and get it working first before tackling the wireless one.
So, if I understood your correctly, when you connect the Mac to the Linksys router directly using an Ethernet cable, the Mac gets a private IP address in the 192.168.2.n range from the Linksys's DHCP service...and this is in the range as defined in the Linksys's administration page for DHCP service?
If so, I will assume that your Linksys's LAN IP address is 192.168.2.1. Correct?
Using Network Utility, located in /Applications/Utilities, select the "Ping" tab, and try pinging the Linksys. If you can successfully ping to it, try pinging to 17.112.152.32. (Note: That would be www.apple.com's IP address.) If that was successfull, then try pinging www.apple.com. If all of these pings work, you should have Internet connectivity. If the last one didn't work, then the Mac is not getting the proper DNS information from your Linksys or ISP.