I literally searched for weeks on how to solve this, so I just wanted to share my solution in case I'm not alone with this issue. It was actually a very simple fix.
The problem: Whenever I turned on my Wii U, whether from the gamepad or the console, the gamepad would enter the menu while the television showed no signal. The console would be "on" with the power light on and the disk moving, but nothing would come up. When I tried to start a piece of software from the gamepad, it would tell me that it was too far away from the console to function.
After powering down the gamepad and the console sepparately, it would then turn on correctly on the second attempt. It was an intermittent issue that did not really stop the functionality of the WII U beyond the first start up, but it was quite frustrating.
TLDR; The gamepad and the console turned on, but there was no signal to the TV. Gamepad could not connect to the Console. everything was fine after restarting.
The Solution: Go to System Settings from the WII U menu. Scroll right until you find the Power Settings, near the end of the menu. The top most items should be Auto Power-Down, and Standby Functions. Disable both of these items.
The Auto Power-Down Function allows the system to "sleep" after being idle for some times
The Standby Function allows the console to perform certain operations after being powered down. This includes the Quick Start Menu that pops up on the gamepad as the console is still in the process of booting up.
I am unsure which of these functions is the true culprit. It could be both, it could be just one, or it could even be just a single Standby Function that is affected by turning them all off. I plan to update this thread with a more definitive solution, but I can tell you with great certainty that one of these settings is the culprit. I do not want to declare one solution to be THE solution until I have been able to do more testing.
I hope this helps someone! This issue was driving me up the wall.