I also have a Troy Built trimmer that is 4 cycle. The same thing happend and it turned out to be the gasket / diaphram inside the carb. I have never been able to find a rebuild kit and they want about $50 for a new carb. Now it sits in the corner and I grab my 18 volt Riobi to do the job. If I didn't have the tiller attachment I would have trashed it by now.

Good luck with yours!

Something is plugging one of the lines either to or from the bulb. The best fix would be to clean and rebuild the carburetor.

I have to assume it is a 2 cycle gas engine. First, check the bulb for splits or cracks. They are replaceable and usually have 2 tabs that hold them in. Release the primer bulb by gently prying around the edge with a blade knife. There should be 2 hoses, usually clear plastic. If one detached or has deteriorated it must be replaced. Second, in the fuel tank on the end of one of the hoses is a filter. If the filter is dirty it blocks the flow of fuel when you try to prime the engine. Gently pull the hose up through the fuel cap opening to find it and replace it.