WiiU owner here.
It looks to me like you are trying to use play only using the gamepad with out the use of the TV. If you are:
Are you playing the gamepad at a distance where the connection from WiiU to gamepad has to go through walls?
Are you playing the gamepad at a very far distance from the WiiU (through walls or not)?
The gamepad does have its limitations when it comes to off TV gameplay. Playing with the gamepad at a distance 30-40ft will cause problems such as lag or loss of connection. it will cause more problems if your trying to play through walls. Try playing with the gamepad at in a closer proximity to the WiiU (5-20ft). If your still having problems It looks as though your gamepad has malfunctioned.
You said that you had your WiiU for just over a month and that you cannot return it to the store. However I believe your WiiU's warranty is still valid for one (1) year since the date of purchase. Call 1-800-255-3700 for Customer Service from Nintendo and they should be able to help you out. Just explain your situation and they will tell you what to do. I've done it before for my 3DS.
If worst comes to worst and you decide you do want to sell your WiiU, I'd look into other places other than Game Stop to trade in your WiiU. As far as I know their trade-in values aren't the greatest. Local game store can sometimes give you a better deal. Also consider craigslist and option too.
Hopes this help, and goodluck!