Might not be the logic board. That ribbon cable is fickle. I ahd this problem and just bought the cable (proximity sensor cable) off of amazon and replaced it. There's a youtube video on how to do it (since it's not immediately obvious), and it's an easy repair. Also, remember to always shut off your phone before you open it. Seems that the proximity sensor or the cable may be especially sensitive to that.
You can also buy the earpiece and cable seperately. You'll need the earpiece, obviously, and the proximity sensor cable. These items together will cost under $10 on Amazon, but will require careful attention to replace.
WHen you make a call and you put the phone up to your face (or cover the phone with your hand) does the screen go black like it's supposed to? If not, and I had this exact thing happen to me, you will need a proximity cable replacement. That's the ribbon cable (#3) that's so annoying to put back together. Apparently it's pretty easy to screw that part up, particularly if the phone is powered on while you disassemble. The earpiece is also connected to that cable, and if the proximity sensor isn't working, nether then will the earpice. It wasn't too difficult to replace.