I can't answer my phone

For some reason whenever my phone rings, it won't give me the option of answering it. If my phone is on but it's inactive (meaning it's in my pocket, turned on but not being used) and it rings, the screen stays off. I'll hit the power button to turn on the screen and when I do that, it sends the call straight to voicemail. If I am using my phone for something other than a phone call and it starts ringing, the screen that gives me the option to answer the call doesn't show up. Does anyone have any ideas of what might be happening and what I could do to fix it?