Droid touchscreen problems and Menu button not working

I'm not sure if this is a Droid hardware problem or a bugless problem, but I thought someone here might have a solution to my problem. A couple of days ago my phone started turning off randomly and wouldn't turn on unless I plugged it into the charger. That problem went away after a couple of hours, and just yesterday my menu button stopped working, completely. Also, parts of my screen don't respond at times.

Is there any solution? Or should I just get my nice raised-keyboard droid replaced for a refurbished flat-keyboard one?

Thanks.