Craftsman Pushmower Starts ONCE with Electric starter and then you have to pull start

I have had this mower for about 5 years. It always key started just fine until this summer. This summer, we would turn the key and it would spin and start ONCE....then, after that, it might start with the key, but more often, we had to use the pull cord. I thought the battery was getting weak and replaced it...It made no difference....it would start the first time ok and then just occasionally with the battery after that..
Looked up everything I could on line to do...did it all...checked the electrical connectors, spark plug changed, air filter cleaned...Made no difference...BUT, we discovered that IF we pumped the primer button about twice before the second attempt to use the electric starter, it would start up just fine...So now overtime we shut it down, we push the primer twice and the electric starter works and starts the engine every time...

In my mind it must be a fuel issue...or not...I would say it was a dirty fuel filter, if it had a fuel filter...
Any thoughts or ideas...???
THANKS..

CRAFTSMAN, 6.50 MRS, Key start, B&S 650, 22", 190cc, #917.376741 self-propelled

Craftsman Pushmower Starts ONCE with Electric starter and then you have to pull start