I've been having the same problem with my Droid X2 which I purchased brand new 3 weeks ago. Every time I'd plug it into the charger, I couldn't use the touchscreen. Then, about a week ago, the phone started shutting off as soon as I connected it to the charger and the phone simply would not charge. So frustrating!!!
I was using my old droid charger, not the one that came with the Droid X2. I tried using the charger that came with the X2 and that fixed all my problems. I compared the two plugs and there is a big difference between them. Now I can use my phone while its charging and it hasn't shut off once.
Hope this helps some of you!