Carrier Heat pump does not come on. Just stopped working. How do I trouble shoot for a bad transformer or other parts related to unit no turning on for either a/c or heat?

To do simple checks like this you do need some tools. A test light, a meter, or a voltage detector might be the best place to start with. I came across the niftiest gadget for trouble shooting, a voltage detector. They work through the insulation of wires. There are several brands. I have a GB Instruments GVD-505A, less than $15 at Home Depot. Touch it to a hot wire, and the end glows red. Find the doodad that lights it on one side, and not the other, and you have the culprit. You do not have to open up housings and expose electrical contacts. You are looking at where your hand is, not where the meter is. Most people are capable of doing repairs and will get it going and not get hurt if they use a little sense. The voltage detector makes it even easier.

Maybe the first thing is to look for a blown fuse on the control board, often an automotive blade type. Check for 24 volts between the R terminal and the com at the air handler.