I was speaking with my professor about this problem, I am curious if someone can get a different answer then what he thought it was. I am not looking for work but maybe an explanation of the answer if the current (I_0) is not 0. Thank you.
How can we possibly tell you if our answer is different than what his was unless you tell us what his was?
The current Io depends on what is connected to the terminals a-b. If nothing is connected, then you have a circuit that has no independent sources in it. Such a circuit is always consistent with there being no voltages and no currents in the circuit, though this solution may or may not be stable. In the case of this circuit it is stable.
Remember that when you have dependent sources in a circuit, you can't just zero out the sources to find the equivalent resistance. You need to apply a test signal to the terminals.