There are several things to consider here.
First, if you took the starter off of the vehicle and had it "bench tested" this is NOT
a good test of the starter. Just because the starter spins during a bench test, DOES NOT
mean that it will have enough power to turn the engine over. The proper way to test the starter is with the starter installed in the vehicle and perform a starter draw test while it is cranking the engine. If it will not crank the engine - IT CANNOT BE PROPERLY TESTED
! In this case, you must diagnose the REST
of the starting system to determine if the starter is at fault. - So to put it simply, NO
- you DO NOT
know for a fact that the starter is good.
Then we have a problem with whatever relay you are looking for. Depending on how your vehicle is equipped, there is an "Inhibitor Relay" a "clutch Interlock Relay" and a "Theft Warning Relay" any of which can stop your starter from working. If your vehicle is equipped with an automatic transmission, the clutch interlock relay does not apply.
The proper way to check all of this is to check for battery voltage at the small BLACK/WHITE wire at the starter motor when you turn the ignition switch to the START position. If battery voltage is present, then all of the relays are working.
You also need to THOROUGHLY
test the battery and perform voltage drop tests on your battery cables to determine if the problem is being caused by a shorted battery cell or a bad battery cable conection.
Please also review this article: What Else Could Be Wrong?