1993 Mercury Force 70hp runing issue

Hello My fathers friend has a Mercury Force 70Hp boat motor and recently it wouldn't stay running. We have changed the plugs to see if that was it but the confuseing thing is that the motor will start and run perfectly fine with the top houseing off but when u shut the motor down and put the houseing back on the motor will start run for 30-40 seconds bog down an quit. Then will not start after that but as soon as you take the houseing back off it fires up after a couple tries and runs just fine,we have checked all the wires to make sure nothing was shorting out and no matter what it runs fine with the houseing off,any idea on what could be the issue? we tried adjusting the air mixture on the carbuerator but no matter what its on it wont run with the houseing on.

almost sounds like a wire is loose and is getting kinked when the hood goes on.

That's what we thought so when the engine was runing with the hood off we gently pushed the wires down one by one with a stick but the engine kept running strong. It's almost like when u put the hood back on its not getting enough air to the carb and smothers it out.