Iphone 4's screen stopped working?

The screen of my IPhone 4 (4.3.5) has stopped working all together. I had it in a Otter-box case and it physically is in mint condition. I had put it down for a few hours and when I pressed the lock/unlock button to read my messages nothing happened, and the screen remained unlit.

I can plug it into iTunes and sync it until the last step of the sync, a error message pops up that says "ITunes could not back up iphone because a session could not be started?". I think that it is a software glitch of some sort...

Also when I switch the ring/vibrate to vibrate, the phone does not vibrate like it usually would to let me know that silent mode has been activated....

Has this happened to anyone else?

Am I still covered under any Warranty although I do not have the "apple service plan"?

Should I reset my phone by holding the lock & home buttons?

Any recommendations of how to get a hold of someone at apple?