You have a CS4 with an external power supply, correct. A friend has a CS4-i with a bad internal power supply. He bought this power converter from Amazon.
The power supply has been tested and it works.
JackHughs
+1
These power supplies are very common, often sold as LED power supplies. I have been using them for decades, as battery chargers, RV power converters, vehicle troubleshooting assistance, etc.
They are claimed to be self limiting in terms of current output (maximum amps), but also have a small glass fuse (Buss-type) soldered to the circuit board. When I set one up for use for other applications, I usually remove that fuse and solder in leads to a Mini fuse or ATC fuse holder that is located outside of the housing. I wouldn't bother for the compressor as the chance of fuse failure appears to be highly unlikely, IME.
These power supplies also have a small potentiometer, usually to the left of the terminal strip. I will try to make time to pull the plastic protector from one of my GX power supplies if someone is interested. The potentiometer is for adjusting the output voltage which can often be adjusted between low 13 volts and just under 15 volts DC.
The little yellow potentiometer adjustment is seen to the immediate left of the terminal strip.
Given that these compressors routinely operate from running motor vehicles, which typically output nearly 15 VDC, an over voltage adjustment of one of these power supplies seems unlikely. On the other hand, DC motors tend not to like low voltage so, like the common protensity of amateurs to want to operate engines at too low temperature, I don't recommend turning down the voltage.
The second photo is, of course, a GX power supply.
The third photo shows the internal circuit board of a generic power supply of this type. The finger points to the glass fuse. The voltage adjustment potentiometer is to the right of the terminal strip and can only be seen as a reflection on the case. The 120/240 VAC switch is center top.