**********UPDATED************
The Linksys WRT54G will not connect to the internet without being connected to a modem.
Is your Linksys connection a secured connection?
If so you will need to know the WEP key to connect to it.
If not, you might consider reading further and making it a secured connection while repairing your connection at the same time.
If you no longer know your WEP key, you can do a hard reset of the router (unplug all wires from the router except for the power wire, then press and hold the reset button... on the rear of the router for 30 seconds) Then using a standard Ethernet cable (RJ45 Connectors) plug directly from your computer to an open port on the back of the router. Open Internet Explorer... its ok if it will not connect to the internet. In the address bar type 192.168.1.1 You will be asked for a user name and passord. Leave the user name blank, enter admin as your password. This will take you to the Linksys Access Page. Now click on the wireless tab and you can name your network. Give it a name you can easily find, write it down. Now set the channel to 11 and click save settings. you should get a page that says settings saved... click continue. Now click Wireless Security. for security type choose WEP for the best safety choose 128 bits you will see a place that says Paraphrase using capital and lower case letters type a word here... a pets name, or mothers maiden name is good.... something you will remember. Now click Generate Key, check to see that Key#1 is the chosen key. Write down the 26 digit key listed on Key 1 line. Now click save settings, and click continue.
Click the Setup Tab. Click on Mac Address Clone, check enable clone address, then click clone mac address. click save settings.
Exit Internet Explorer and disconect the lan wire. Now unplug the power wire from the router, and modem wait 2 minutes, Plug in the modem and wait 1 minute, plug in all the wires into the router, then plug the power wire back in.
Are ya tired of this yet??? Don't worry... you are close to connecting and having a nice secure connection too.
I'm assuming you are running Windows XP
Click Start, My Network Places, \Yhen on the left side of the window that opens click View Network Connections. Right click on the Wireless Network Connection and click Properties. Click the Wireless Networks Tab. Check Use windows to configure my wireless network settings. Now click View Wireless Networks. Choose the network name you created on the Linksys page. You should then be asked for the WeP key... this is the 26 digit key you wrote down earlier enter it and make sure that it is set to use Key 1. click apply or ok to close and you should be done. close everything and restart your computer. It should automaticly connect.
On your Xbox 360 console... Turn it on, press the large button in the center of your controler then press Y to enter the dashboard. Scroll right to System, go to Network Settings, Edit, and enter the network name you just created, you will also need to enter the Wep Key that you wrote down earlier as well. Your default gateway should be 192.168.1.1, subnet mask 255.255.255.0
Once you have entered all of your settings save them and click on Test Xbox Live.
I hope you find this helpful and not too long winded.
Good Luck, and feel free to contact me if you need further help