1996 Mitsubishi Eclipse New battery, but car doesn't start

I just installed a new battery, one recommended by the Autozone computer. It is bigger than the previous battery and the positive cable didn't reach to the terminal, so I put on a Post Terminal Battery Cable Splice to extent the cable. There was one spark when I connected the cables to the battery.

Now, the engine does not start or try to start. Other things happen too._The dome lights stay on even when they're turned off with doors closed for extended time. When I turn the ignition._Oil temp gauge goes to top. _Windshield wipers go on and stay on when in the OFF position. _Radio doesn't power on to enter the code. _The starter seems to buzz for a quarter second then stop. _Radiator fan goes on. _Head/tail lights work. _Brake lights work. _Horn doesn't work. I checked the fuses and they seem to be okay.

I've replaced the battery before without problems, but this is way out there.