Chainsaw Repair

Hi everyone! This one seems pretty simple to me, but over the past few days of working with, and on this saw, its causing much frustration. 

Saw is a stock 350, about 6-7 years old, run with factory settings, routine cleaning and maintenance.  About two months ago I would start it up using choke, fast idle, kick it down to normal idle and let warm up and commence working with it. Well about that time, it would start taking longer to start.  Maybe 15-20 pulls before it sputters and I could high idle start it.  And about 2-3 minutes after a normal idle, you could pull the throttle and it would start to go but then bog out and die.  So basically as soon as it was warm it was dead.  Restarting was momentary at best.  Long story short, it would then start and run without the top cover on.  The air filter was still there, just the orange plastic cover was the only factor.  Change the plug, change the fuel lines, new air filter, nothing.  Even took the air filter off, but as soon as the top cover was back on, its as if its starving for air.  The side of the powerhead is clean, no restriction in the airflow there.  Any ideas? reset carb to factory settings, but even with tinkering with that, it does nothing.

Steve

Boot looks great, took it all down and put it all back and it still looks great.  It runs literally like a dream without that darn cover. I mean it runs like it should. So tempting to just drill holes all throughout the thing!! Any other suggestions? Obviously its an air restriction problem, but it doesn't make sense. Right?