Seems like you've decided your next move. I just hate a mystery with no ending or answer
When you factory reset, did you restore your Google account right away when the device came back on and went through initial set up? This would likely include your settings and Applications backup, and may re-add the issue to the clean device.
Waiting before re-adding your accounts after a factory reset helps eliminate a lot of variables.
If you power the phone down completely, what do the lights do? (make sure you aren't in Fast Boot or Power Saver before power down)
A hard restart might be worth a try. Press and hold down the power key for 10 seconds. You may see the capacitive buttons under the screen start to blink or a message come up with a countdown to reboot. This method forces the hardware and software to more fully restart.
You could give Safe Mode a try as a last effort:
(This will run your phone with all 3rd party applications disabled on a more clean configuration.)
Ensure that Fast Boot is turned off in your Power Settings
Power the phone down and wait for it to be fully turned off for a minute or two
Power the phone back on
When you see the white HTC Boot screen immediately press and hold down the 'volume down' hardware key on the right side of the phone. Hold it until the phone completes start up, and you see the words "Safe Boot" displayed in the lower left corner of your lock/home screen.
To get out of Safe Mode simply power off and power on your phone as normal