Goodness ... what "part" is it? Maybe some of us "internet scroungers" can locate one. Do you have the part number etc? Can't imagine what it could be.
Even a controller board can be found online as I replaced one in my 14 yr old Carrier unit's compressor for $40 a few years ago when the useless home appliance warranty service couldn't even figure out what it was (needless to say I immediately cancelled them). Found it on eBay. There aren't that many parts.
Edit: They replaced the fan motor, contactor & cap and nothing helped. I even told them it was the board but they "know better." Only thing left was the circuit board. That fixed it. I even bought a spare.
