My 2006 Kia Sedona is overheating and the A/C is blowing hot simultaneously

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I had service garage recharge my A/C 200 miles from home. 60 miles from home the A/C quit and the engine overheated. Once cool I removed the radiator cap and saw no water is moving across the radiator. I towed it home, removed the thermostat and saw water moving across the radiator. Thank God there were no bubbles in the water and my oil is old and dark. I think the water pump is working. The fans can work with direct power, but do not with normal connections. The relay connection next to the power supply on the Fan Controller (25385-4D0900) was corroded. I cleaned it. the connector on top of the compressor was found lose and rubbed in half on the Compressor pulley. 1st- I need to find where in the wire harness the power stops to the cooling fans. Is there a way to physically check the fan controller with a meter? Is there a way to check the in-line relays? 2nd what do I do to check the connector of the a/c compressor? 3rd -After the cooling fans are running, what should I check first on the A/C issue?