Network question from a mac noob

Hello everyone. I am new to this forum and this is my first post here. I am not a regular mac user but I have always admired them. I am not real familiar with all the mac terminology either so forgive me if I sound a little vague. Here's my question. I have a friend with an imac running os x 10.4 that has always been just a real basic computer user and I've always helped him out with any settings or changes he needed to make. His friend next door to him has wireless broadband and wants to share his connection with him via his linksys router. They are very close and the signal is strong - almost 100% bars in the connections dialog. He asked me if I could look at it for them because they couldn't get it to connect. The connection is already setup using "Airport". I went over and my friend Bob turned his imac on - First I just opened Safari to see if it was working and it immediately connected to the internet via the "Airport" connection they had already setup. Bob said all it would do the day before was dial on the modem. We used it for about 10 minutes and it had a really fast speed, then all of a sudden, we couldn't get anywhere in the browser and the modem started wanting to dial out on his old dialup connection. We looked in the connection settings and the wireless connection said "connected" and showed signal strength with the bars almost 100% - still for some reason now the browser only wants to look at the modem. We unplugged the phone line from the modem so it couldn't dial to see if it would use the Airport connection instead but it just gave us a 'no dialtone' message. It's as if the wireless connection is there but Safari only wants to look at the modem. I'm not sure why the wireless connection worked for a bit before the modem started dialing. Unfortunately none of the 3 of us are very advanced mac users and are not sure what the problem could be. If anyone has any suggestions for us it would be greatly appreciated and I thank you in advance.

Moved to more appropriate forum.