It sounds like you have a leakage path somewhere in your system. My first thought is that your transistor is not fully turning off. Check that it's base is being driven low, and that no other circuit elements might be causing it to get voltage on it from a small current leakage. Adding a pull-down resistor, like 100k from base to emitter, might help?
Can you provide a schematic of the circuit you are using? Something drawn up in Paint would even be a place to start.