We have two stihl chainsws 009 &044 at the moment they will only start if you add fuel to the carby and then will not continue to run. We have checked main and idle jets and the diaphrames seem intact ,spark is okay. Could compression be the problem
could be compression. I dout it, I would check the fuel filters first. You can pull the fuel line off at the carb. fuel should pour out, with a little shake, of the saw. If the compression was no good, you stoll could not start it easy, if at all.
The fuel screen in the inlet side of the carb is the most common cause in my experience, take off the side with the one screw in it, and see if the fine mesh is clogged or partially so, only way to cure is to replace the screen.