I too have the same problem onethatknows has. The Homelite uses a metal strap wrapped around the chain pulley. When the handle is pressed forward the strap tightens and the blade stop, usually stalling the engine.

The problem I'm having, and I think he is, is when the brake handle is back, in the off position, the band is still pulled tight against the pulley.
there are two ways to identify this. 1. Pull back on the brake handle. The chain will move freely, even with the engine idling. 2. If the saw will run at full throttle, and you oil pump is working, you will notice burning oil. It's caused by the excessive friction between the brake and the chain.
The brake is supposed to be a little tight at all times, this prevents the chain from moving when the engine is idling. Safety thing you know.
One thought I have is it could be the clutches on the chain pulley wearing out. But, I'm not sure. yet.
I'll post any solution I find, and hope to read your solution. Other than buying a new saw.