sport jet 120 idling issues

Hello, I am new to boats and learning the hard way LOL. I have a 1995 Sea Rayder F-16 bought it not running. got it running great and took it out a few times. put it back in the water after letting it sit for a couple hours to take it out again and it wouldnt start. it would fire every 3rd or 4th try but would not stay running. i played with it a while and got it to start by advancing the throttle to about 1/3 and it stays running (this is about the time it starts to move the ignition trigger and all the linkages attached to it. as long as i dont let that linkage come back i can keep it running. under normal driving situations it will die as soon as i pull the throttle back to about 2500 RPM. plenty of power as long as i dont back throttle down to where that linkage all starts to move. The stator is new, battery new, starter new, and lanyard kill switch is new. any help would be awesome! Thank you