How can you tell if you have blown a transformer? Also, does anyone know where I can find a part number for my transformer without being able to get to the part itself? I have a model number of 58PAV. The circuit board is HK42FZ009. I believe it is Carrier but not 100%

If you have 120 V from the house wire connected one one side, and don't have 24 volts on the usually red and blue wires on the other side, the transformer is shot. Check for a blown fuse. It may be in a fuse holder inline or on the circuit board.

I lost several transformers on my old furnace. The last one I bought was a Radio Shack 273-1512. At that time I bought a 270-1238 inline fuse holder. I had to replace some fuses, but the transformer lasted several years until I replaced the furnace. When I tore it out, I found a place where the chipmunks had chewed the thermostat wiring.

Those transformers are a fairly standard thing. Just make sure a replacement has as high or higher rating as the old, and it is protected by an appropriate size fuse. The 273-1512 has a third secondary lead you tape up and leave unconnected.

How can you tell if you have blown a transformer? Also, does anyone know where I can find a part number for my transformer without being able to get to the part itself? I have a model number of 58PAV. The circuit board is HK42FZ009. I believe it is Carrier but not 100%
Check the fuse at the transformer before condeming it. It is a 3 Amp...

EDIT: A bit late on the reply...

The transformer that LABMAN said will work good.
Most of the time a transformer goes bad is because the T-stat wire going to the outdoor A/C system is shorting out. Check to make sure that it is not damaged. Dogs love that wire for some reason!

http://www.photolocker.net/images/Labman/KatetheAC.jpg

How can you tell if you have blown a transformer? Also, does anyone know where I can find a part number for my transformer without being able to get to the part itself? I have a model number of 58PAV. The circuit board is HK42FZ009. I believe it is Carrier but not 100%
The best way to test a transformer is to remove it from the circuitry. Test for continuity on the primary and secondary they should read very low ohms, if either read open the transformer is bad. A transformer is nothing more than two oils of wire wrapped next to each other. As the electro magnetic field expands and contracts in the primary loop, it induces voltage to flow in the secondary loop. Most transformers print the color of wires for the primary and secondary, the color codes aren't exactly universal since it can be for 120 or 240 volt systems.

Hope this helps.