It may be moot at this point, but start with a harsh thorough vigorous soapandwater cleaning ... for example, a weak or shorted ignition can sometimes be completely cured, merely by cleaning the oil film and sawdust/mineral grime off the spark plug wire, the cutoff wire and switch, the plug connector spring, and the plug.
Before pulling the carb to rebuild it, clean out the carb box and covers, so no stuff gets inside the intake opening.
For my 2-cents, bidding on an ebay saw should start out discounting that the saw is going need
(a) a harsh cleaning inside the oil and gas tanks *including the vent valves, inside the fuel, oil and pressure lines, and everywhere else you may never have thought of before ;
(b) a carb rebuild (new diaphrams and metering valve) $10 ;
(c) an oil pump rebuild $10 ;
(d) a new sprocket and probably a new clutch and maybe new clutch drum and bearing $5-$40 ;
(e) a new brake band and retainers $15 ;
(f) a new spark plug $3 ;
(g) a new air filter $15 ;
(h) a new fuel filter ($5) ;
(i) a bar dressing and probably a new nose sproket $15 ;
(j) a new chain, especially if the existing chain doesn't want to cut straight, say $10.
After that new crank seals, then new top end, piston rings, pistons, cylinders.
I'm the first to admit, 'tis still fun!