I don't think that this will stop you unlocking, rooting and flashing a custom ROM. Actually it might fix the issue.
The issue might be a hardware issue although I doubt it.
Try it in Safe Mode:
Turn fastboot off in your power settings.
- Switch off the device.
- Power it on
- Once you see the HTC splash screen, press and hold the Volume Up key till the phone boots up in Safe Mode
Where did you get the phone from?