Here I am looking at trying to put my 026 into service. I cut up maybe 3 or 4 trees when I first bought it ages ago because they were laying on my farm field and now am getting ready to start cutting fire wood so I need a saw again. I don't even have any chipped paint like I saw in one of those pictures. Mine does have the riveted name plate on the engine cover and the winter / summer air selector is a screw on piece that you remove, rotate and reinstall. It has probably been at least 20 years since I last started it and I was coming here to see what I should do before even trying to start it when I found this thread at the top of the forum section. As far as an unfiled chain, I have one of those but I also have an OEM spare chain for the saw so it may have run more than the one referred to above, or maybe not. Frankly it has been that long ago that I forget why I bought it. It may have just been my conservative nature to have a spare. My guess would be a carb kit and fuel and impulse tube replacement. I pulled the plug and it looks just fine for a used 2 stroke plug. (Yes I used to ride 2 stroke bikes so I know how they should look.) When I found it in its storage case the plastic hinge on the case failed when I tried to lift it by the handle. There is a puddle of B&C oil in that case, maybe an ounce. There is also maybe an ounce of premix in the fuel tank. So, is it time for me to charge out and get a carb kit and a couple of pieces of tubing or do I drag this to a dealer for service? No way am I going to expect it to just start for me. It was always cold blooded even before I stopped using it.
OK, where do I start? I am not afraid to do a carb rebuild. I have watched a couple of videos on the subject and it looks far easier than all that float drop stuff and complicated clearance templates I have done on car and bike carbs. Do I even bother trying to run it or just assume the ethanol has ruined anything plastic or rubber exposed to it? Exhaust side is a different matter. By the time fuel gets there it is nothing but CO2 and smoke. I can't imagine much damage on the piston/cylinder parts or even much wear on the clutch and drive components. The thing just does not have that kind of run time on it.
I think you have figured it out pretty well, carb kit, filter, fuel line, impulse line and at least a careful look at boot between carb and cylinder. flush the fuel tank of course. If you really don't want to bother with it send it to me. I will even pay shipping, but don't expect to ever see it again.
Ethanol shouldn't be a problem if it's been 20 years since it ran. I would clean the fuel tank out and check all the fuel lines for cracks and leaks. Maybe throw a new spark plug in it and see if she'll start.
I would try it as is, with fresh fuel mix of course. 20 years ago there may not have been ethanol in your fuel. I've poured fuel in saws that are 40-50 years old and they have fired up and ran. They were not perfect, some needed a carb adjustment, some needed a cleaning, and a few needed more extensive work. But if you get it to run, you have an idea of where to start. A carb clean/rebuild and fuel line replacement on an 026/MS260 is a piece of cake.
X3 on what was said above. Going back to pre ethanol, I would try it as is. Then maybe just clean the carb. The fuel line and impulse are pretty straightforward replacement parts.