I'd like to ask you to try a test first and see where we should start. POur a half a teaspoon of mixed fuel directly into the spark plug hole and then try to start. Do not use the choke. Let me know how it turns out.
Ok then you have an issue with the low speed circuit in your carburetor. I am willing to bet that you have a welch plug inside the carb that is no longer sealed. If the welch plug is dislodged or unsealed then the low speed circuit will not work at all. The high speed will still work because it uses both circuits mixed together (the purpose of the welch plug is to separate the circuits) Unfortunately with todays fuels the sealant that was used 3 years ago is no longer able to hold up to the chemicals found in todays gas.
You will need to replace your carburetor in order to fix this problem. The good news is that the carburetors being built today use a stronger sealant, so hopefully you will not have this problem again.
Here is a link to find an authorized service center near you.
You can also probably go to your closest small engine repair shop and they should be able to get you one. You may also do an internet search for makita carburetors and find one on line.
If you know that you are working with a known good carburetor then the other possibility is that you have a bad crank seal. You have one underneath the flywheel and one under the clutch for the belt. They should only be about $10 each and are relatively easy to replace.
If the carb you are using from the other saw works on this one, does the carb in question work on the other saw?