What is wrong with my car?

Did the solenoid on the starter click when you tested it cause if you had lights and no clicking it sounds like the solenoid is bad. Your have power because of the lights coming on. If the solenoid is bad you will just want to get a whole new starter anyway. A new starter is usually 80 and a new solenoid is 75 (just a ballpark guess). Last thing is to check if you've got power going to the solenoid wire on the starter, this will be a small wire going to the starter and will only have voltage when the key is in the start position. If there is no voltage check the fuse going to it and then the switch is the last thing to check.