Car won't start after replacing battery and starter

Hello. My sunfire wouldn't start friday morning. The car turned the lights on and radio like the battery was good, but it wouldn't start when I turned the key. I got it to start after a jump, thinking nothing of it, and it started immediately 3 times afterward that day. After those 3 times, it wouldn't start again and did the same thing. I jumped it again, and again, it started. It started immediately twice the next day, saturday.

Sunday morning, my car wouldn't start again, doing the same thing it did friday morning and afternoon. After a jump, though, it still didn't start. We took the battery to Autozone and they said it was bad, so we bought and installed a new battery. Still wouldn't start, so we had a neighbor who works with cars look at it and said the starter was bad. We got a new starter as well, they connected it, and it still wouldn't start, with the car doing the same thing as earlier in the day. All the lights would come on as normal and the radio but it just wouldn't start. My neighbor says that the car is drawing power from something because the plugs that go into the battery spark a little when you first insert it into the battery. They were going to work on it more today. Any help with this is much appreciated, thanks!