I might have some suggestions.
So it sounds like you do have power coming in to the compressor control unit, right? But then after that, it's not working. (I'm not 100% clear on exactly how/what is not working.)
Do you have access to the connections on the compressor control module? Presuming this is a Danfoss/Secop BD35 or BD50 (those are the only two I have any experience with), the terminals on the module will be flat blades (with wires attached) and each position will have a label with a Letter code or a "+" or "-".
I'm not there, but I would start by doing two things (of course being sure there is incoming power to the control module):
1) Jumper to eliminate the thermostat. Electrically "jumper" terminals "C" and "T" on the compressor control module. This will overrule the thermostat and (if that is the problem) the refrigerator will run continuously without shutting off. If so, great, because this is easy to deal with. If you have a mechanical thermostat, there are inexpensive and fantastic electronic thermostats you can install instead (or replace in kind). If you literally have "nothing," it doesn't seem like it would be this, but easy enough to check.
2) Set up a test light which may show various error codes based on number of flashes. To do this, wire a small LED bulb between terminals "D" and "+" on control module. See if there are any flashes, and if there are, count them. (Or I think you can also use a meter and count needle movements, though I have always used a small LED bulb.)
BTW, you can wire up such a bulb permanently if you like, for future use. I have a little bulb with clips on it.
If you go ahead with these two things, what do you get?
PS: Just out of curiosity, what is the model of the control module? This will be right up at the top of the label that has the letters and the connections. I have an 11-year-old Vitrifrigo, and just for example, mine uses the 101N0500 control module (which would now be replaced with a 101N0510, last I checked). They all seem fairly similar though.