1994 Camry fans are not working?

1994 Toyota Camry I replaced the radiator and now my fans will not turn on and the engine begins to overheat. I replaced the thermostat switch which is on the bottom left hand side of the radiator itself and I also replaced the coolant thermostat that is on top of the engine behind the radiator hose. The funny thing is when I unplug the wiring harness on the right side the fans both come on? Also when the #1 fan relay switch is barley plugged in the left fan runs. Any thoughts? The next thing I was going to do was replace all three of the relay switches but they are very expensive.