My GF's daughter has a Desire C, and dropped it off this morning reporting the following;
It started playing music without anyone doing anything this morning, and the screen wouldn't turn on. The only way they could get it to stop was pulling the battery.
Replaced the battery and the phone wouldn't start.
I read up a bit and left the phone on charge (no LEDs showing) for 2 1/2 hours. Came back, still couldn't boot.
I took the mains charger out and plugged it into my PC USB and tried volume down + power - still no boot, BUT, the screen did lighten slightly...
So, I WAS thinking the phone was bricked, then, as I was typing this and retried the plug into PC bit - the phone has booted
I was going to delete the post, but decided it may be of use to someone, so I added 'solved' to the title.
In a nutshell: if you have this issue, be patient - it might not be the end of the world (or phone!)