The fact that the solenoid is clicking proves there is a complete circuit to the solenoid from the relay. the relay serves this purpose....The starter switch cannot carry the necessary amperage the starter needs without being a very large heavy duty item so the designers came up with a relay. The starter switch goes to the relay which then goes to the solenoid....the solenoid carries the heavy amperage needed for the starter...this is why one of your battery cables goes directly to the solenoid and the other goes directly to the starter.The starter switch activates the relay which in turn activates the solenoid. if all the wiring is connected with clean and properly sized wiring to handle the current (Amperage) then the connection is made and the necessary amperage flows to the starter. The fact that a direct connection to the starter results in immediate starting means that the fault lies in the wiring from the switch, relay and solenoid. Check this wiring AND the associated connections for corrosion, make sure the connections are clean and there are not frayed wires. Look for wiring that may have a few broken strands but is still connected at the end where a connector is. Partially broken wires like this will allow a connection but can't carry all the current needed for proper operation. Your VOM will show conductivity but the resistance will be high so always check both when checking wiring with a VOM.