1995 Hyundai Sonata hesitates to start

I recently bought a 1995 Hyundai Sonata automatic with 96000 miles. The car always started right up when I test drove and for the week after I bought it. I put it in to get serviced (replaced front ball joints, left upper control arm, windshield). It was in the shop (ie. not being driven) for about two weeks. Now that I have it back, it hesitates to start. The dash lights come on immediately when the key is turned, so a battery problem is not likely. The car just makes kind of a whirring/grinding sound when the key is turned and eventually starts up and runs normally. It is much easier to start once it is warm. Also, when the car is cold, it shakes violently in reverse. The check engine light comes on intermittently; sometimes for a few minutes, sometimes just for a second, sometimes not at all even during a long drive.

The seller told me that the spark plugs might need to be replaced soon. Could this be the problem, or is it larger?

Thank you!