I purchased a used condenser unit from a reputable hvac dealer/installer last year, but only this year got a chance to install. Everything as far as I know was hooked up correctly, but when the thermostat is turned to a/c the contactor engages but absolutely nothing from the condenser. The blower runs inside but not even an attempt for the compressor starting up. I also checked for current after the contactor, and this is where I get confused, when the contactor is NOT engaged there is power at both terminals on both sides of the contactor! It's probably very simple but I'm too frustrated to figure it out. It's 220V by the way.

Does the outdoor fan run or even attempt to run??

No, neither the compressor or the fan.

That sounds like you are not getting 24 volts to you outdoor unit

It is getting 24 volt that kicks in the contactor but because it's already got current at all 4 terminals before the contactor is engaged is what's throwing me for a loop.

What are you using to check the voltage, is it a read out meter or is it a light. You need something that will give you a read out.
One other thing for you to check it the capacitor, is it a dual capacitor, meaning does the fan and the compressor operate off the same capacitor? If it is a dual one check the capicator, look at the top and bottom, see if there are any bulges at all. If it is misshapen at all it is possible that it is the problem.
Check your wiring and make sure that you have the incoming power on one side of the contactor and the compressor connected to the other side of the contactor.