Saw won't start without starting fluid.

SOURCE: Echo CS440 wont idle when warmed up

Check for air leaking at cylinder to block.gasket.

SOURCE: I purchased a Stihl 036 chain saw at a yard sale.

CLEAN OUT FUEL LINES

SOURCE: Homelite Timberman chainsaw won't run anymore

Sometimes the transferred metal feels like compression.
The volume of most chainsaws is so small it makes a HUGE difference in the reading; depending on which end of the compression tester the Schrader valve is mounted (should be spark plug end). If the total cylinder volume is only 2 cubic inches and the hose adds an additional cubic inch you can see how it will impact.

FF
I recommend you join here:
ArboristSite Chainsaw thread (free to join)
http://www.arboristsite.com/forumdisplay.php?f=9
There are some threads about using acid to remove metal transfer from cylinder walls. There are some Homelite collectors. There are a bunch of good people that enjoy lending a little expertise. I am not a Homelite guy, I have done some research for Homeys and often you must buy an entire short block.

You may find this helpful too:
Homelite/Ryobi.com (authorized parts supplier)
https://www.gardnerinc.com/recons/disclaimer-lg.php - Agree; Choose “Product Line”; “Select OEM” & “Select Catalog” both to “Homelite Consumer Products”. A drop down list appears; self explanatory from here.
The numbers Homelite & Ryobi use do not match the numbers everyone posts. A careful inspection of your saw should find something that matches.

FF
your question impressed me so much I almost did not answer. It is so though and well thought I though you had been at this for a while and knew exactly what to do next and were pulling my leg. Good on you. You will be welcomed at ArboristSite. Good Luck
Lou

Testimonial: "Very thorough and helpful feedback"

SOURCE: husqvarna 51 died and wont restart

hi
if you have a good compression,a strong enough blue spark and carburetion for the fuel air mixture try priming the engine(put small amount of gas in the spark plug hole)then start the engine.If the engine runs only the gas you put inside the cilinder there is a carburetion problem to find and fix.
let me know regards savumihai71

SOURCE: This saw will start maybe

Hi Jack, I will try to help you out. As far as the high/low screws go turn them in (clockwise) until lightly seated so no damage is done to the needles or the seats. Now turn them both out 1 turn but also remember the position so you can go back to it if you have to. That is the suggested basic adjustment. The saw should run at this setting and sometimes is bang on. If everything is OK with the carb only minor adjustments should do it. When adjusting go 1/8 turn at a time. Because of idle problems start with the low speed mixture needle. Turn out (counterclockwise) 1/8 turn and try running your saw. Do that 5 or 6 times, if no good results go back to starting position. You might try the high speed mixture needle the same way to see what happens. ( Always remember the starting position of the adjusting screw) The one thing to be careful of when adjusting the carb is not to adjust the high speed needle less than 1 turn out (counterclockwise) from a lightly seated position. The reason is you don't want to run it too lean (less gas more air) which could damage the engine because it could overheat. The gas and air mixture also helps with cooling. Try any adjustments as long as you don't go too lean.
Inside these types of carburetors there is a mesh type filter which is very, very fine, so if anything even dust gets in, this mesh will stop it, so it is something to check out, it is a common problem. You say you took the cap off the bottom, that is usually the metering side. It is critical that the diaphragms (membrane as you call it) be installed very accurately.
From what you describe you did a very good job of checking everything out, so what could be needed is a carburetor overhaul, unless it is something that is intermittent, which is a pain. I hope I have helped you out even a little. All the best and good luck.