Chainsaw Repair

I've never had a problem with my 5 year old Stihl MS 310 until recently. The usual start procedure when cold is 3 or 4 pulls in the full choke and high throttle position which usually causes the motor to fire. Then a pull in the open choke and half throttle position will cause the engine to run and then on to normal run and low throttle . However, the engine now fails to even fire in any of the choke and throttle positions. I've installed a new spark plug and gaped it to .02" as specified in the manual, and ignition spark looks good. I replaced the fuel mix  with fresh ethanol 91 octane unleaded gas mixed with Stih's 50:1 synthetic 2 cycle oil. I replaced the carburetor with a new OEM Warbro carb and also replaced the air filter with a new one. I did notice that the fuel line to the carb was under a lot of pressure because it shot fuel about 5 feet when I pulled it loose. The only thing left that I can think of is the timing and cylinder compression. I've ordered a compression meter and will check that eventually. I'm guessing that the pressure should be somewhere around 130 psi , but I couldn't find the spec on it. The timing lock on the flywheel breaking or slipping  seems unlikely.  What have I overlooked here ?  Is there something else that I can check for this problem ?

I tried the fuel squirt test before I placed the post. the engine still didn't fire. Also, the fuel that shot out when I removed the carb and attached lines was actually the impulse line rather than the fuel line. The line had to be ok or the pressurized fuel in it would have gotten out prior to pulling it. I notice that when I pull the spark plug after pulling on the start rope a few times, the plug is wet with fuel. I must have a flooding issue also.

Thanks for your input...I'll definitely try your suggestions in the morning - hope it works.

Well, the saw is finally running. After going through every step suggested, it still stubbornly refused to fire. I decided to give it one last try before giving up on the thing. I pulled the carb and the 2 connecting lines and and  a vent line (I guess) back to the  tank.  Verified that the vacuum pulse line  and diaphragm pump in carb were working and the fuel line and filter were clear - could hear the air pulse activate the pump. I sprayed Sea Foam through the carb ports and blew air into the ports (although the carb is new) and cylinder chamber.  Then put it all back together and cranked it 4 times in full choke and high throttle and it fired - open choke and half throttle got it running. Apparently lots of oil residue in the chamber because of much white smoke from the exhaust. But, it settled down and ran well.  I'm using 91 octane ethanol free gas in every small engine that I have now in the hope that I'll have less of these problems in the future.  I appreciate the help that I received here in troubleshooting this problem.