Talking of chainsaws, I left a saw in the back of a pickup some 6 or 7 years ago and forgot about it because I had bent the handle on it and broke the side bracket.  Couple days ago I seen it inside the topper and wondered if it still had gas in it and it did, and didn't smell bad. Tank was 3/4 full. Despite the upper handle was off, I gave it 5 pulls and it was running. Found another handle and started using it. dang, I sure like that old Jonsered 52E... Despite the chain is worn out and will be getting a new chain soon on it. 

 Bet an electric saw wouldn't have started up after sitting that many years... and still be quieter than mine if it did run.  But then it wouldn't be running on Av gas either.  Think I better switch back to that stuff again, because it didn't form any crud in the tank in all that time either.

Sheesh, 5 pulls?  Must be nice!  My dang Stihl sits for a half hour and it's 10.  But there's nothing wrong with it.

Sheesh, 5 pulls?  Must be nice!  My dang Stihl sits for a half hour and it's 10.  But there's nothing wrong with it.

I have the same problem with my Stihl.

So... when it takes several pulls, the USUAL situation, is that the fuel pump diaphragm (the largest neoprene part in the bottom of the carb) is starting to get stiff from age, and exposure to fuel-type stuff.  Ethanol will get to 'em pretty fast, but even good gasoline/oil mix will eventually wind up with bad actors in it, as a result of chemical action between it, and the various materials the fuel has been in contact with.

On newer saws, the other issue is mixture screw settings...   The 'emmissions' aspect of design protocol force manufacturers to put 'limiting caps' on mixture adjustments (or in some cases, eliminate adjustment altogether), and one of the issues, particuarly semi-hot starts, is that the fuel mixture is too 'lean' to fire until you've pulled the cord a bunch.

The other things that will, if the saw is well-aged, is

 - crankcase seals... specifically, around the crank, and the crankcase halves.  The crankcase is responsible for generating the vacuum to draw fuel/air mix in from the carb, and PUSH the fuel/air mix into the combustion chamber.  An air leak in the crankcase totally foils that.

  - plugged exhaust screen.  The muffler has a fine wire mesh screen whose function is to catch sooty embers and hold them to prevent starting a forest fire.  Unfortunately the screen eventually becomes plugged up, and won't flow exhaust.  An engine that cannot flow exhaust, will not take in air/fuel mix to fire... hence, they don't start well... and frequently get weak on power.  Pull the muffler cover, yank that screen, and see if it'll start well without it... if it does, clean the screen.

If a chain gets jammed and bent, the drive/guide tabs inside the bar groove won't line up, and it WILL throw the chain.  Bending 'em back is a temp fix, and if done well, will oftentimes last 'till the chain teeth can't be sharpened anymore.... but realize that a maligned drive tab will frequently bind as it passes through the bar (the 'good tabs' will all be in line, and the bad one will still be slightly offset), so it'll wear out the bar quickly, and overheat it, and the bent point, rather fast.

Throwing on a new chain solves much anguish.