This is going to be an unpopular suggestion, but my aging dad did it out of necessity. He could run a saw for about an hour a day, if he didn't wear himself out trying to start it. A squirt of what I named "Old Man's Helper" i.e. starting fluid, the saw would start in 1-2 pulls every time.
If you've got the primer bulb, make sure the carb is primed, give it a quick squirt of starting fluid, and otherwise start it normally. You're not running the saw off the starting fluid, just giving it a rich fuel mixture to ease starting.
Still have both saws, 026 and 036 Stihls. They both ran fine last time I fired them up. I really should take them out and cut some wood with them. (Yes, if triggers a memory with anyone about a previous thread of mine, I know the 026 is a 50cc saw, just what I'm looking for, but I'm OCD and I want a "red" one to go with my 2166. The 026 and the 036 are a matched pair... Really I should get an 044 as the 70cc saw... Aw now my OCD and CAD are playing off each other!)