Radio installation problem

Hi,
I have a 93 gmc Sierra with 92,000 miles, 350 5.7 liter engine. I recetly bought a new head unit/radio and was going to install it. So I unplugged the negative terminal from the battery. Then cut the existing wires to the old radio and cassette player. Then I hooked up the new radio and hooked up the negative terminal to the battery and the truck starts up and the starter keeps going, all without the key in it. PLEASE HELP!