I pulled in the driveway it died and would not start again

I had a lot of corrosion on the battery and cable terminals. So bad I had to cut the positive and use one of those adapters bought at a parts store. I decided to try that before replacing the battery. Once I put the adapter on the car started fine and I drove around the block but when I pulled in the driveway it died and would not start again. I took the battery to auto zone and sure enough it was bad. I purchased a new one when I went to install it I realized they had sold me a marine battery. I accidentally touch one of the battery terminals with a cable and the horn sounded like the alarm was going off. I went back and got the right battery but when I turned the key absolutely nothing happened. No sound, nothing. The interior lights work, headlights come on bright and a few other lights, The car will not shift out of park and the brake lights do not come on though. I have tested every fuse I know and the starter relay.

Any suggestions as to what the problem is?