Factory reset will remove that account from the phone. Of course that doesn't delete it from Google's servers, just removes it from the device.
As for the rest, since we don't know what you did in your failed rooting attempts we can't say exactly what is wrong. Best bet may be to find a ROM Upgrade Utility for your device, download it to a PC, boot into the bootloader, put the phone into fastboot mode, connect to the PC by usb and run to RUU. That will flash the phone with a complete new set of software.
You'll need someone who knows this device to suggest the right RUU. It will depend on your region and network (if bought network branded), so it would help to know those. Shipped-roms.com is a good place to look, but you'll need to know HTC's codename for the device rather than the name it is sold under (easy to Google, but as I'm typing on TapaTalk as I'm on my way to work I can't do that this second).