desire safe mode and rebooting.

If a factory reset doesn't solve it, that usually indicates a hardware problem.  My advice would be to send it in for repairs. 

Did it recently come into contact with water?  Like making a call in the rain, or even putting it in a damp bathroom?  Those are known to damage the phone and void the warranty.
I'd suggest taking out the battery and looking for the water damage indicator.  If it's white, you'll probably be ok, but be careful if it's red.

It's a small sticker that changes colour if it comes into contact with water.  Normally it's white, but as soon as it gets wet it turns red.

It should be on the side of the battery, next to the 3 copper connectors.

The Desire is known to have issues with water.  We have quite a few topics on water damage here, including topics from people who sent their phones in without knowing that there was water damage at all.

As for repair, if a factory reset doesn't sort it out, it's almost certainly a hardware issue.  I'd get in touch with HTC if I were you. 
However if there is water damage, HTC simply doesn't repair phones because it'll be cheaper for you to just buy a new one.

thought i'd do a bit more googling before contacting orange about this and come across a user who had a similar problem and managed to get it out of safe mode by powering it up with the trackball held down. this worked for me too and the power button now does what it is supposed to do again.

happy days
hope this helps someone else

rob

I am brand new to this forum, I found this thread through a search for this problem.  My phone landed in water two days ago, grabbed it quickly, took it apart removing battery and both cards.  When everything dried, it didn't want to boot up and finally I got it in safe mode.  Then I couldn't get it out of safe mode and the power button caused a reboot, I followed the instructions found here (holding the track ball down when powering up) and the phone is restored.  Thanks.

PS The white label on the side of my battery has some pink on it and the home button no longer works, otherwise the phone seems fine.