I'm at a 10 ton trane roof top unit.I'm getting power to the contactor and the thermastat is calling for cooling but the compressor or fan motor is not coming on.There are two boards that I'm not familiar with.How can I check to see if one of the boards is fried?

If the unit is running in cold weather than there is ice building up on the coils located outside. This is normal in that the unit is running in heat pump mode heating inside and cooling outside, After the unit detects the ice build up it briefly reverses the cycle heating the outside coils melting(defrosting) the ice which you observe as water on the pad.

The video gives you an example of the defrost cycle!
2012 Trane XL15i Heat Pump Defrost Cycle Steam Show

Here is what to do . Pull out or turn off Electrical disconnect behind unit . Carefully remove panel covering controls in unit . Note most units have a flat panel with a few screws, but some GE units have a welded metal box on top of unit which needs to be removed. After exposing controls. replace or turn on disconnect. Then take a plastic handled screwdriver and push in on center of contactor (boxlike part with a lot of wires hooked ) If the compressor now comes on release contactor , and check for 24 Volts AC at base of contactor where thermostat (small wires that run on outside of black refrigerant line ) with thermostat on and calling for cool you should measure 24 to 28 volts . If voltage is present replace contactor after disconnecting from power. If no voltage go inside , remove cover from thermostat, and check for 24 volts between red ( R) and yellow (Y ) terminals on thermostat , If voltage is present , replace thermostat , no voltage check voltage in heater / air handler if you have voltage at air handler , replace thermostat wire from heater to thermostat / if no voltage check for blown fuse in heater , this should be either an inline fuse or an automotive type fuse plugged into circuit board (with power to heater disconnected check broken wire or black mark in fuse when held up to light. If fuse good turn on power to heater and check for 230v to one side of transformer, if you get voltage to Primary (incoming side ) of transformer, check output side of transformer for 24 - 28 volts. If transformer shows input but no output replace transformer after turning power off. If you heard a buzzing or grinding noise , when pushing in contactor , but compressor didn't start look at run capacitor (this is round or oval shaped object with wires going to contactor and compressor ) Looking at area where wires plug this should be a flat surface , if it looks domed shaped or bulging out , it is blown and needs replaced , use same mfd rating and 440 Volts to be on safe side. / If there was no noise from compressor when contactor was pushed in , put your hand on top of compressor (black object in center of unit ) If hot , allow to cool for at least three hours with power to unit turned off and retest . If compressor comes on after cooling , check for bad fan motor in outside unit (it may make a squealing or wining noise and stop runing for a while , also check for / clean outdoor coils
Hope this helps .
Thanks,
Alex

Check the unit to see if the outdoor fan and compressor are coming on. If not, check to see if power is reaching the contactor, both the high power contacts and the low voltage solenoid. Some contactors can be manually actuated, and a quick press (with a NON CONDUCTIVE ITEM) can show you if the contactor is engaging. If the solenoid is not working, check the wiring of your thermostat. When set to cool mode, there should be voltage on the solenoid of the primary contactor, sending power to the outdoor fan motor and compressor.

If the outdoor fan and compressor engage normally, then make certain the coils are free of debris and other blockages. If air flows freely and the compressor is running, feel the tubing for temperature changes. One side should grow cooler and the other warmer.

If the compressor runs but there is no temperature change, take your unit to a certified technician to check for leaks and system pressures. Roof top units typically use R22 refrigerant not R134a automotive refrigerant, which require EPA certification for purchase and dispensing.

Than it's not wired correctly. Did you splice the motor wires? Black on left, common to cap which should be the right from contactor and fan which I think, without looking, is brown. purple common...

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This could be a lot of things, there is a contactor relay in the system that might be bad, there is a possibility the contactor is not getting voltage, there could be corrosion issues with connections or a bad start capacitor.

The contactor for the compressor and outdoor fan is activated by your thermostat when you call for cool. The small coil is an electromagnet that gets 24VAC when you call for cool at the t stat. The red wire in your T stat connects to the blue (or sometimes yellow wire) in the t stat completing the 24VAC circuit and closing the contactor. The line voltage is supplied to the poutdoor fan and compressor upon the contactor closing.

You can manually pushthe contactor close and the outdoor fan and compressor should start. Do this with your hand on the insulated portion of a screwdriver and take the tip of the screwdriver and push the contactor closed. The compressor and outdoor fan should start. That tells you that you have a thermostat to contactor coil issue if the t stat does not close the contactor when you call for cool.

If you don't here the compressor kick in after about 3 min then the thermastat is not telling the compressor to com on, or the control board is not telling the compressor to come on. The power can be traced from thermastat to the control board and will have a 12volt feed on the yellow wire at the control board with compressor mode on. From there it is 120volts the control board has a relay that turns on the compressor. the compressor capasiter can cause the compressor not to come on, normally it will have burnt wiring.

It could be the capacitor, it could be a loose wire connection, it could be a delay switch or a contactor/relay.

the system is wrong, the blower must run continuously , and the compressor is the will stop if the temperature setting is reached. The outside fan is the same as the comp.

open the service panel to check for control voltage of 24volts when tstat calling, The contactor should be pulled in, if contactor is down,and contacts appear to be clean, and the unit is still not running, it is a bad compressor. to test this unplug the black wire from the compressoror at contactor,w/ power off! Turn on power if fan works normally it's a bad compressor. However if you see a swollen split cap(5 wires to a soup can looking w/ the terminal C,F,and Comp), switch it first and start at square one.
You also need to consider the high pressure switch if its cycling on off on off.