One thing to note is that the compressor winding resistance test is not a definitive test. It will tell you if the compressor is bad but does not tell you that the compressor is good. It may have winding to winding shorts or mechanical problems.
Sounds like it is a meter reading problem re: you are on the wrong resistance scale.
If this is one of the auto-ranging type where you cannot select your resistance scale then I also would hate it.
K usually means kilohms *.000 so a reading of 1 is 1,000 ohms
M usually means megohms *. 000,000 so a reading of 1 is 1,000,000 ohms.
For instance my meter has the following scales.
200, 2K, 20K, 200K, 2000K and 20M ohms.
To measure the compressor coils I would use the 200 ohms.
This scale measures 0 to 200 ohms anything over 200 ohms shows as an open circuit / infinite ohms.
Lets say I try to use the 20M scale then the meter will show all windings as 0 ohms (dead short) because the meter does not have enough digits (resolution) to show the low resistances of the compressor coils.
The resistances should be just a few ohms.
Below is a good site on how to check the compressor coils.
How To Fix a Refrigerator - Appliance Repair Guide - ACME HOW TO.comIf your meter is a pain to use then perhaps just replace it.
You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
There is a good post on meter use at the top of this forum section.
Below is my usual blurb on meter use.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.
There is a good STICKY at the start of this forum about it's use.