IMac Wireless Connection Failure

[Suziekay]

I have an IMac OS X 10.5.8. It's about 4 years old. Recently I subscribed to a DSL through AT&T and purchased an At&T modem. The AT&T tech support was unable to help me set up my wireless connection. My AirPort in on and I have a full bar signal. My network has a check next to it. When I turn the AirPort on, it automatically comes up with the network. There is no way to remove the check next to the network unless I turn the AirPort off.
The issue comes when I disconnect my ethernet cable. I loose my internet connection. The AT&T tech support told me to contact Apple but my computer is older then 90 days.
Also, I have an I phone that does the same thing. My wifi connection works everywhere I go with no issues but will not work in my home. All the wifi bars are up but it says connection failed. Please help

 

[Matthew Yohe]

You didn't really tell us about your network.

"When I disconnect my ethernet cable"

Which ethernet cable?

Tell us how your network is wired.

DSL <- Connected to -> Airport?

Give us more.

 

[Suziekay]

More Information

I am using a new 2WIRE AT&T modem. My mac is connected to the modem using an ethernet cable. I am using a DSL line through AT&T.
While my ethernet cable is connected my "air port" settings are turned on. I have all bars. When I open the drop down menu on my WiFi signal icon it reads:
Airport ON.

2WIRE727 (727 are the last 3 digits in the SN#) (there is a check mark in front of 2WIRE727)

I am unable to remove the check mark. When I try to highlight or open 2WIRE727, the airport box closes.

The bottom of the airport box reads:
Join Other Networks
Create Networks
Open Networks Preferences

When I disconnect the ethernet cable the airport (wifi) setting and indicator stays the same but I loose all internet connection.

My WiFi worked until I changed modems.

The same thing is happening on my IPhone. I have my WiFi on. It shows my network, 2WIRE727 and I have a full signal. BUT I can not connect to the internet. My WiFi works everywhere else but in my home.

I know nothing about computers. My son took care of these issues but has left for collage. I would appreciate any help.