All right guys, it was an hardware failure.
I reopened my htc and checked all the connectors and (re)placed some of the yellow tape. After the reassembly, my phone just works as it should. All problems are solved.

My HTC HD2 also got the keys stuck after only a week of use. T-Mobile is sending me a replacement phone today.
Is this a common problem? I'm afraid it may happen again.

Hey guys I'm having same issue. Going to try opening up and check connectors.