I have an Amana Model RCE30A2B Compressor unit installed it is about 6 years old, the compressor will not cut in when demanded yet the cooling fan for the unit does

When you say cooling fan I assume you mean the outdoorfan?
Sounds to me like your capacitor could be bad, or compressor could be on thermal protection. Could you give us more information. Like sounds, times of day, is compressor trying to start?

The contactor pulls in and I have the correct voltages either side of the contactor. My multi meter does not allow me to test capacitors. The compressor does not even try to cut in only the cooling fan for the outdoor unit, it assummed because the fan was running it had not cut out on over heat or one of the pressure trips is this correct

Depends.. some compressors have a 90 minute thermal protection if it trips. And if it goes on locked motor amps it will trip thermal protection immediately and you will not notice it.
Easiest thing to do is pull capacitor, but make sure to take picture and draw yourself a detailed wire diagram. Take it to grainger or somewhere to be tested. And if need be get new capacitor. Caps run from $20 to about $20. If that does not do the job than it is time to call a hvac tech out.

Thanks for the information I shall pull the capacitor and have it tested. This was a great help.

Also with power off check the power wiring where it goes into the compressor itself. Many times one of the 3 wires will corrode/burn off and the compressor will not run. You may have to depress or pop the clip that holds the cover on over the compressor wires.

Thank you very much this is exactly what the problem was, after being quoted $1000 for a new compressor I revisited the problem and after your input repaired it I am now back in the Florida air conditioning thanks to you

Was it a wire burnt off or the compressor? If it was the wire there is a special kit available to fix it if it happens again. Let us know what it was.

Thanks for the input, it looks more like the connection had corroded causing arking and eventually failure. New terminals have done the job, if I get another 8 years out of the unit I'm happy.

Yep the connections can become corroded and cause problems.