This looks to be a somewhat common problem with HTC devices .
If you Google for
htc desire frozen screen You will find that many people have run into issues like this.
The most common solution is to do a reset, however that is what Shiloob Vm has already done.
I would then suggest trying to find the cause of the problem by going back to basics.
Remove all of the extra things like headphones, chargers, SD cards, SIM cards.
- If your device works without anything extra then add them back in one at a time rebooting each time to narrow down the culprit(s).
- It could very well be that two or more things working in conjunction are causing this problem so try many different combinations to make sure you know what the problem is before replacing that part.
“The strongest of all warriors are these two — Time and Patience.” ― Leo Tolstoy, War and Peace