Windshield wipers not working properly

A faulty wiper switch will cause these issues.

I have a leak in my sunroof, and after a particularly rainy day I had a good amount of water in my car. Well my amp in under my seat and eventually fried it. It was so bad that while my car was off the speakers were booming static and would not stop unless I disconnected the battery. It smelled like burning electronics. I eventually disconnected the amp and took the radio fuse out of my car. The booming static stopped but I still notice a few weird things. My back windshield wiper is not working anymore and I noticed that I can still roll down my windows for about thirty seconds after I turn my car off. I am worried that there is still some electrical issues and I am going to have a electrical fire. I drive my car a lot so this really worries me.

Running the windows after the ignition switch is off is a "feature" designed into many cars.

Put the radio fuses back in and see if the rear wiper works. Rear wiper circuits usually share a fuse with some other circuit that you will notice immediately if it stops working. Otherwise the wiper motor or wiring to it could short, blow its own fuse, and you would never know it until you needed it. It is a safety thing.