Notebook Wireless and Networking

My problem is this HP spectre laptop will not recognize or connect to the ATT wifi in my home. This has been an ongoing problem for over a year and I have read every forum and tried every tip I can find.  I recently updated my laptop/windows by an automatic update and had wifi connectivity for 4 days. Then it suddently stopped connecting.

My wifi will connect to every device in my home. So ATT says it is an HP problem. But my laptop will connect to every wifi I try, hotels, hotspot on my Verizon phone, wifi at work. So it seems my wifi networking card works just fine. 

The problem is my ATT wifi and my HP spectre laptop will not talk to each other. And it is very frustrating that I have a wireless HP printer that won't work unless I am connected to the same network, which is ATT wifi.

I have removed and installed the device driver numerous times. I have tried the release/renew option numberous times. Removed the wifi connection numberous times. Updated everything I can find. On a rare occasion, maybe once every two weeks, it will connect.  

Mostly the wifi just says Cannot Connect when trying to connect from the systray. Since the windows update, it asks for password, but when I put in password, it just keep asking again and again and again for the password.

Since I have had this problem our family has bought two other laptops and I did not choose HP because of this issue. Our Asus and Samsung laptops work fine with wifi. I am ready to throw this laptop out the door and start with a different brand of laptop. 

Any additional thoughts or ideas to try would be appreciated. 

Thanks, 

Net