Try to charge the battery before you do anything, first in a jump start, extended jump if it doesn't take, then with a charger if you have one, on a trickle charge overnight. Barring that, take it out and bring it into walmart or the like and they will test it for you, and sell you a new one if need be.
I don't know about collision braking systems, but cars do have a diagnostic thing that plugs into the fuse box under steering wheel usually as I'm aware, that will give you the error codes if you can find someone with them, you can buy one for a hundred or so as I'm aware, that are good for ranges of vehicles not entirely sure.
Oh yeah, for the corrosion, take off the terminals before you do anything, and clean them with emory cloth, or sandpaper, or something scratchy to get any funk off of it, both the connectors and the terminals.
I once replaced a good battery with a worse one, after it wouldn't start, and later learned one of the terminals was somehow chronically loose, and just threading a screw in the gap to make it tight fixed it. That replaced battery couldn't be returned as the original was gone by then, and itself failed just the year before last, only making it maybe 4 years.