Internet connection problems via WRT54G wireless router

I’m new on this site and for some reason my first post isn’t showing up. Hopefully it will this time.
I have Earthlink as my provider. I run the Internet through a wireless router which is connected to my desktop. The connection here is almost always okay.
My laptop is the issue. Every now and then my laptop loses the Internet connection and won’t re-connect. I don’t remember what I did last time to make it work unfortunately. The laptop is picking up the wireless signal (excellent quality) and says it is connected to the router. But I can’t connect to the Internet. Can someone help with this? I need it explained in layman’s terms if possible 🙂
Thanks in advance.