Originally Posted by opus
Sounds more like a bad ground to me.
Starters are grounded through the block and the current only flows one way through them. You would never see a difference in behavior from an open/compromised ground versus an open/compromised power side. This is different from other things like power windows which reverse current through the switches or computers which, lacking a proper ground, can overlay voltages on network wires to other modules on the vehicle.
A loaded voltage drop test will quickly diagnose a bad ground or power. With someone turning the key to the "start" position (VERY important...current must be flowing for this test), put the red meter lead on the battery positive post and the negative meter lead on the huge battery cable on the starter. You have created a parallel path so you should see no voltage. Any voltage that is present is voltage taking a path of lower resistance. I wouldn't be surprised if you saw .5 volts on the power side but if your meter is indicating more you have excessive resistance on the hot side. If it reads battery voltage your solenoid is not working, be it because of a lack of signal from the key or a faulty solenoid itself.
If the power side passes, perform the same test on the ground side by putting the red meter lead on the body of the starter (get a clean spot) and the black lead on the negative post of the battery. Again, .5 volts or so is normal.