damage to the engine but it can short out the battery, blow the fusable link, short out the alternator or mess up the computer ! about all i can tell you is hook up the battery the right way and see if it will start and run !

Nothing to the engine. But you might have blown the main fuse or fried the computer.

None to the engine but the alternator could be damaged.

Engine nothing but computer may be blown.

None. You could have blown up the battery but you would have already known if that happened.

Sooooo, the car you jump started it with didn't have any lights?