We've been having air condoning problems where our unit would freeze up / leak water. We brought out a tech to have a look, the indoor and outdoor unit was completely forzen. Once thawed, he said the unit was low on refrigerant and he wanted to look for a leak. After 3-4 hours of searching and no leak found, his 'manager' came out to double check and found the 'leak' in 5 minutes and decided he wanted to replace a coil and a 'blower board' just incase to 'to not take any chances' (our blower works completely fine). A few things to note, the tech said there was little to no refrigerant in the system. He also said he put nitrogen in the system to find the leak.
In an effort to double check, I took a look at the outside unit, turned off the power to our unit, lifted the fan and I noticed one of the wires going to the compressor is disconnected (the wire connecting to the bottom circle-like opening in the picture below). Additionally, all but one of the screws holding down the fan to the outdoor unit are missing, so running the fan, causes strong vibrations.
The exact model/brand of our compressor (different than shown below) is a Copeland CR42K6-PFV.
What I am trying to do now before shelling out hundreds of dollars for a fix that may not be required, is check if the the issue is much more simple than what we're told (my gut tells me it is).
My question is, what are some things I can check/try in order to troubleshoot the icing of the unit? Would plugging in the wire described and adding screws to the unit and turning on the outdoor fan be a smart thing to try? are there any risks to doing so, other than the unit icing?
I appreciate any advice