I have tested the capacitor and it is fine, how can I test the transformer to see if that's the problem for the blower fan not starting up, it tries to start slowly but no luck then the coils freeze up. I noticed the handler had iced up and after thawing it out then noticed blower fan will not start up. Any ideas.
Thank you,
Kelly.

Relay

The first thing you want to do is not run it in 'cool' mode when testing it out and troubleshooting. If you keep freezing that coil up and liquid refrig gets back to the compressor than the repair will quickly add a 0 on to the end of the tab.

instead use the 'fan' on mode on t-stat

the transformer etc is a dead end because you have control voltage at the t-stat.

the relay could be a problem (low probability) because they usually stick on or off. No in between.

can you disconnect the wires from the fan motor and test the voltage there on a demand for the fan at the t-stat?

you should have 120 or 240 what ever your air handler uses. If so and the run cap is positively good than your motor is bad. Can you give the motor a budge (without losing a finger or two) to get the squirrl cage going?

when you check the voltage at the motor make sure you are getting the voltage you need and it is also not dropping off