Can get an Internet ID on my wireless network

Hello,
I just go a new (new to me but otherwise used) Gateway Laptop. It is an M350WVN, 3 mhz P4, 1 gb, XP SP3. Firewire port, wireless card, and ethernet adapter are standard. I am not using Firewire or Ethernet.

My system recognizes my router and has excellent signal strength. It will not, hower, connect to the internet. It gets a message of "limited or no internet connection".

I've tried the usuals - rebooted, reloaded all drivers, made sure Windows in configuring the connection and run "repair" on the connection. My hardware device screen shows all hardware to be up and running.

This machine worked for a while on a secure network and then stopped and hasn't worked since. It also worked on an unsecured netword after much effort. I have no idea what made it work or what made is stop working on either network. I have 3 other machines on both networks and they're doing just fine.

Need a real expert on this one.

Thanks in advance.

Mike