Hello Shay, Good morning. I first may ask if you have rooted installed a new rom on your device, I was looking around and found quite a lot of people with this same issue, maybe its a long therm problem created for pushing people to buy newer devices, :)
I found this little guide telling how to calibrate it: http://www.rahinur.com/android/how-to-ca...
I dont have any HTC device so I cant really test it. Off course if you cant even pass the lock screen than I am bringing you to false ways, xD
You could try to hard reset and see if it solve, apparently using Htc sync:http://www.htc.com/us/software/htc-sync-... will allow you to backup your stuff from the computer without having to use the screen.
for a Hard reset of your device,: http://www.thefullsignal.com/htc/htc-des...
And if the hard reset fails could be that a Digitizer cable either unplug or broke inside, and if you are feeling confident tear it apart and check it out.
The only video I could find was this one: https://www.youtube.com/watch?v=pj2rhucq...
It may looks bad quality but I guess it is enough.
Now if the digitizer is broken I found this one on ebay: http://www.ebay.com/itm/Replacement-Touc...
I maybe took the wrong Htc Desire, so check it out it matches your phone if you that motivated to fix it.