help w P0627 error code

Question

My car ran out of gas on Monday I thought it was a oil issue because my gas guage read 1/8 th of a tank of fuel and I hadnt checked my oil in a while nor had I had an oil change. I added oil because it was low and the oil and check engine light came on when I ran out of gas. After getting gas it ran fine that night and the next morning. Then that afternoon it wouldnt start. I hear one click and then nothing. I got the error code P0627 from the odometer but we checked that cuircut and its fine. Need help please!!