How can I test if my wireless router (WRT54G by Linksys) is working before connecting it to the cable modem?

I'm just going to assume you've followed directions but you can't get the internet but do find the router on your wireless (local network only). Reset your modem. Make sure if it has a backup battery to unplug that too or it will not reset. It will be on the side or under the modem. I've found this is the biggest problem with cable modems.

Connect Modem [wired] to Router [wireless] to PC.
=
* DO NOT REMOVE POWER TO RESET NETWORK DEVICES *
-
Set router POWER OFF.
-
Reset modem: With a straightened paperclip, press RESET button momentarily.
-
Wait 60 secs.
-
Set router POWER ON.
-
Reset router: With a straightened paperclip, press RESET button momentarily.
-
Wait 60 secs.
--
PC Command Line:
-
Click [Start] - Click [Run...] - enter: cmd, Click [OK]
-
At the prompt (c:\.....>) enter: ipconfig /release, press [ENTER]
-
At the prompt (c:\.....>) enter: ipconfig /renew, press [ENTER]
-
TEST: Open Web Browser: Connect to Internet.
--
If SUCCESS: Repeat Steps after PC Command Line on other PCs.
-
If NO SUCCESS:
-
At the prompt (c:\.....>) enter: ipconfig /all, press [ENTER]
-
Ensure DHCP Enabled == YES
-
If IP Address == 0.0.0.0 OR 169.254.0.0 to 169.254.255.255, connect Modem [wired] to Router [wired] to PC and perform ALL steps again.
-

hook up the router to your computer. port 1 of the router goes to the nic on the computer. its obviously not going to assign a valid ip address due to the modem is not hooked up. you might be able to get a 169.254.x.x ip address and you might be able to obtain a 192.168.1.xxx ip address but you will be unable to get online. why go through all that trouble you might as well connect your modem to the internet port on the router and your router to your computer reboot both devices and your computer machine and it will assign an IP to your router via dhcp from your ISP and then your router will assign the ip addresses on your internal network via dhcp from the router itself if it is turned on which should be by default.

yes, you should be able to connect it, and it will assign your pc a local ip address.