If it's a universal transformer 115v,208v or 230v do you have the line voltage right. You can wire it up using the wrong wires and it will not produce 24v. If you have 4 wires on the line voltage side check them.

The transformer showed as an OEM replacement 120v - 24v. I think I reversed the wires at first, but then changed it to the correct and still nothing.

You have a transformer for a 115v system(gas furnace), and you don't have a electric fan coil that needs 230v to work right. If all is true and you have a 115v to the two wires going to the transformer and you don't have 24v at the two that are leaving it you blew another transformer.

Yep that is what I figured, so what could cause that? The wiring at the T-Stat was a 5 wire configuration, would adding the/a jumper wire cause this or would it have happened due to putting the wires on the Transformer incorrectly or both?

Ok,

Here is the newest discovery... The new part # for the Transformer has the wires or at least the connections reversed. There are male end connectors on the Transformer for V-in(115v) and V-out(24v), on the old Transformer the 115 went to the large male connector while the 24 went to the small. On the circuit board the connector (which can be seen in the picture on page 4) shows the wires coming out, my NEWEST question is do those wires just pull out of that connector? If so I am going to reroute the wires to the appropriate locations, (small end to the right one) noting the schematic on the door and such.

Any issues with this idea and will they simply pull straight out of that connector with a pair of needle-nose pliers? A/C guy wants $120 to "rewire" if that is all it needs?