The cable going to latch under the hood appears to have broken or disconnected. It is connected to the lever under the dash so I believe that the problem is the latch under the hood. How can I get the hood open without damaging the hood? My goal is to change the battery.
I’d try to pry open the latch using a long, thin screwdiver. The latch is located (as in most cars) at the front center of the car, tight to the hood when fully closed.
You need to open the hood to repair the cable, as well as to replace the battery, check and add oil and other fluids, etc., so don’t worry too much about the condition of the hood (or the grill) so long as you get the hood open. But you should be able to pry the latch open - if you can see it - without damaging body parts. Use a flash light and get at the latch the best way you can. Be patient and inventive.
I have never attempted this, but it seems like it might be a little easier if the grill were out. The grill is held in by two little quarter-turn locks at the top. If you can reach in through the grill with a wire or something to turn them, or pull off the plastic panel down below behind the front bumper and reach up and turn them, you may be able to get the grill out.
Pulling off that plastic panel down below might be a good way to get a look at the hood latch whether you get the grill out or not.
Having an identical car parked next to yours with the hood open is my best advice. I have fabricated all manner of hardware using that method.