I have a Trane heat pump and air handler. When I select heat, the blower does NOT run, but the outside unit fan turns very slow and the breaker trips. Do I have a problem with the handler blower or the outside unit? Should the handler blower run when the thermostat is selected to "ON" regardless of the outside unit, or are they connected via a circuit board? Thanks for any assistance.

When you put tstat on fan instead of auto,, the fan should run,, even without the H/P not running,check or have someone check all your power connections,to me good and tight,especially the grounds, the kicking of breakers is not a good sign,, when did it last work right? when the heat pump runs, the air handler fan should run at same time,the blower not blowing might be causing the h/p to kick breaker from too much high pressure,, don`t try to run till repaired

You may have more than one problem. Starting with the easiest. Turn the heat, off, cool switch to off. Turn the fan auto, on to on. If the blower doesn't come on, check the breaker to the air handler. If you have a meter, check for 24 volts AC between com and G at the air handler. If not, check your connections at both ends of the thermostat cable. See https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html
Make sure the thermostat is wired up correctly.

If everything is OK, you may have a bad board or a bad blower motor. It is a pain getting to the contacts on the circuit board. With a voltage detector, you can just jab it into the wires running to the blower motor. If it lights up. And the motor isn't running, chances are it is bad.

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.

Update on this problem. The blower motor was cooked. I replaced it and the air handler now works fine. The Heat Pump still attempts to start when I reset the breaker, and then it eventually trips the heat pump CB. We determined that the compressor is internally shorted to ground, and it is history.
Since it is winter in Florida... I don't need the AC, but I occasionally need some heat on a chilly morning.. (50 is cold down here ;) The airhandle has heat strips, so I still have a very primitive heat system for now. Time to save some cash to replace a tired and old system. Thanks for the troubleshooting help.