2004 660 running poorly

Hey guys,
I have a 2004 grizzly 660. The four wheeler is all stock. I’m having a few issues with it. first issue I’m having is it is running poorly, it will idle fine and full throttle is fine but when you get into 1/4 to 1/2 throttle it starts to pop out of the exhaust. I took the carb apart twice and cleaned all the jets twice and added a inline fuel filter just in-case there is something in the tank. I replaced the spark plug and the plug cap and still no improvement. So i figured I would adjust the valves. Intakes were really tight and the exhaust were not to bad. still no improvement and now my starter wont turn my engine over so I checked my valve clearances again and they are all correct. Intakes are set at .10mm and exhaust is set at .15mm. I got the motor to start after i adjusted them i had to pull it over by hand because my starter solenoid failed right after i tried to start it. So i tried to jump the starter and it still wont turn the engine over.

Is it possible my starter was weak and with the intake valves being so tight it was giving it some compression relief??

And as far as the popping is it possible that my air/fuel screw is not set correct?

any advice will be greatly appreciated thanks for reading.