Arduino with cell phone
Here's a test I would do before I tried to replace the button with a transistor: check to see whether the closing of the circuit pulls the joined contacts high or low. Once you know that, you can design the right replacement circuit.

To explain a little more: when the button is not pressed, one terminal will be high (3.3 V, maybe?) and the other will be low (0 V). When you press the button, does the low one get pulled up to 3.3 V, or does the high one get pulled to 0 V?

If you're trying to pull a terminal low when you should actually be pulling the other terminal high, I don't think the circuit will behave like you want.