I'm thinking that anything that is polarity sensitive might have been damaged, including the engine control unit. The voltage regulator and alternator diodes may have been blown.
altanater is junk
Check headlights and dashboard lights first. If no/minimal power for the lights then replace battery.
You could have a short in your electrical system, your battery might need a charge or be replaced.
because the battery is the source of the power for the headlights. there could be an issue with the battery or the alternator can be failing.
Cranking slow can be caused by a weak starter, dirty or failed battery cabled
If terminals of the battery are reversed, it will short the device that is using the battery. On a car reversing the cables can blow fuses, melt wires, and fry computers.
the problem is in your high beam switch. there is a short in it and it needs to be replaced
Check the fuses
Interesting?? I had my starter and battery replaced on my 2002 Saturn VUE and within a few months my low beams ands daytime running lights went out. Dealer says the post in the fuse block is burnt and the entire block needs to be replaced at a cost of over $600.
Sounds like your alternator and battery need to be replaced soon.
You have the connections reversed.
Did you install a fully charged battery of the correct group size and connect the cables securely? Did you incorrectly jumpstart the car with the cables reversed and break things before replacing the battery? Did it turn over before you replaced the battery?