1999 Ford Escort Car won't start

We had a few real cold days (live in Buffalo, NY) and the car started like usual, without problem.
As the cold spell broke (ok still cold) the engine would hesitate at first rollover, then fire up and run fine. (Did this for 2 days) With the starter hesitation - like it wouldn't rollover at first, but as soon as the engire would turn it turned over at normal speed; getting slightly worse. Yesterday afternoon, it rolled over and but won't start. I checked this morning and I don't think I have fuel on the rail. The car seemed to roll over better this morning. The battery was taken to autozone and passed the load test. So my guess is the starter is probably bad. Could the starter draw cause the fuel problem or am I looking at two different failures.