I had the same problem for two weeks. I was about to send in the phone to the warranty company Square Trade when they suggested a hard reset (reset to factory specs). It took 10-20 minutes followed by reentering email providers and I'm back in business!
This is not an actual solution, but so far I am having success with being able to answer my phone. I downloaded an app from the android market call "Easy Answer Button". When a call comes in and your screen is locked two buttons actually show up, one that says "answer" and one says "decline. So far so good it works really well, I have been able to answer my phone when calls come in and the screen is locked...no more dragging down to answer and up to decline.
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