Note that you will only have 12 v power available at the starter side of the starter relay when you are cranking the engine. You can check the relay by putting a meter across the 12 v in and 12 v out terminals, with the wire to the starter disconnected. If connected to the battery it will show 12 volts, when the key is in the start mode.
Sounds like the problem may be elsewhere, and perhaps on the circuit from the ignition switch.