How to switch an external circuit with Arduino?
If I understand your writeup correctly, this is what you have built:







simulate this circuit &ndash; Schematic created using CircuitLab

What you didn't mention in your question is that you made a connection from Arduino ground to the base of the transistor and the seconds circuit's ground connection. I drew the extra lead 'loose' for illustration only, but you see where it should connect. Current needs a return path, it is not sufficient to only have the forward path (from Arduino through R1 and base-Q1). The return path is emitter-Q1 to Arduino-GND.

Do notice though that the two batteries / power supplies must be floating with respect to each other otherwise you're going to short them out.