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Assuming you're wanting to run it at 120 volts, 1 & 3 to one of the source wires, 2 & 4 to the other. Doesn't matter if 1/3 is black or white from the source.

Wire colors of the windings mean nothing, it's the numbers that matter.

You may have a burned field coil or armature coil. Do an ohm test from lead 1 to 2, and then 3 to 4...the readings should be close to each other, and relativity small. Also do a reading from each individual lead to ground. None of them should show any ohms. If the reading(s) are low, that coil is shorted to ground (or leaking to ground).

If you get a reading between 1 to 3 or 4, you should get a reading from 2 to 3 or 4. That may indicate that the armature is connected between the coils.

You may have found 3 wirenuts because the previous owner had it wired as 240v. 1 would be to nut 2 to 3, 1 would be 1 to the source and the third would be 4 to the source.

This is just general info to get started. If you can disassemble the motor you can get better testing on each piece and look for damage.

Nice write up Kyle. Almost as if an electrician wrote it. ( Tongue in cheek) Couldn't have explained it better myself.