Heat Pumps and Electric Heating - Heat Pump Transformer

Hey guys I have fairly good knowledge of the refrigerant side of the systems and my EPA card but electrical is not my strong point. I have a approx 8 year old Miller 4 ton heat pump the contactor will not pull in, the unit works when the contactor is pushed in by hand. I checked the voltage at the contactor and have 18 volts I checked the voltage at the transformer leads it looks like I have 4 leads two have 110 volts I assume incoming voltage and on the other two I have one that has 18 volts and one that has 5 volts. The model number/wiring schematic and any other info are unavaliable due to adverse enviromental problems in the installation area (the creek apparently covers the unit about every three or four years LOL) I am assuming that the transformer is bad so I am planning on replacing it my question is how can I get this unit back in operation temporarily untill the correct parts have been ordered (100 degress and high humidity) My thought was that the lead off the transformer with 5 volts probably feeds the defrost board (some electronics requires 5 volts?) and that the 18 volt side is for the thermostat to contactor which should be 24v. Can I just purchase a cheapo 110 volt to 24 volt transformer and wire it in. I do not have a account with a Miller supplier in my area and it may take me a few days to get the correct replacement part. I am assuming that if I jumper from a 110 volt source to the new transformer that I can just feed the 24 volt power back into the lead where I am reading 18 volt on the existing transformer which should be feeding the thermostat would should rthen send 24 volts to the contactor and pull that puppy in. Note: I have several years of experience with the refrigerant side and about 26 yrs with the ductwork side I have a real nice Fluke multimeter/Fluke Amp probe and wiring kits other fun stuff, just limited in my control knowledge any pointers would be appreciated. Oh by the way I know that I could just tape the contactor closed but would rather have it working correctly as it may be several days before I can get the parts and we do want to freeze the coil on the silly thing and risk compressor damage.

You should check the secondary leads of the xfrmr together and see what you get. It sounds as if you are checking them to ground. You should have 24 vac coming out of it + or - 10%. If you need a new xfrmr just make sure it's of the same or higher "VA" rating.