AT&T U-Verse TV service on a TV dictates the specific channels and extra features you have on the TV, but doesn't affect the TV's most basic functions, such as turning it on and off. Troubleshooting a TV with U-Verse service that won't turn off requires you to troubleshoot the TV itself, rather than any aspect of U-Verse service.
Remote Control Issues
One possible reason your AT&T U-Verse TV doesn't shut off is if you are having remote control issues. Most basically, your batteries may be dead and need to be replaced. Alternatively, you may be using the wrong remote to attempt to turn off the TV. If you are not using the remote that corresponds with the TV -- for example, you use the one for the U-Verse receiver -- the TV doesn't turn off. It is also possible that the remote provided by U-Verse doesn't have the proper remote code for your TV. If this is the case, contact the TV manufacturer to get the proper remote code for your TV.
If you are not experiencing problems with the remote but, rather, find that the TV doesn't turn off when you press the "Power" button, the problem may exist with the Power button. A good way to test this is by attempting to turn the TV off with the remote control. If this is successful, your Power button is not working and needs to be repaired.
Unplug the TV
If your TV still doesn't turn off after troubleshooting the remote control and the Power button, a more serious electrical or wiring issue exists with the TV. To turn the TV off in the interim of getting it fixed, so as to avoid the TV burning out of being damaged further, unplug the TV from the wall outlet or surge protector.
Seeking TV Repair
If a problem indeed exists that prevents your TV from being turned off while it is plugged into a power source, you need to procure repair services. Contact the TV manufacturer directly for free repair if your TV is still in its warranty period. If it isn't, locate a nearby television repair specialist and bring the TV in for repair.