Starter troubles

I have a 1995 K1500 and receantly replaced the battery. When I hooked up the new battery the starter started spinning with out the key in the ignition. I later pulled the IGN B fuse from under the hood which solved the problem and the truck starts and runs like normal but apperantly the IGN B fuse also runs the AC and power windows. Could anyone tell me if I have a blown relay or short in the wiring some where and how I can fix it. Any help would be great because I'm really confused. Thanks.

Do you have a remote starter on it? Sometimes remote start systems will activate when power is disconnected and reconnected.