Hello, welcome to JustAnswer.
If your motor runs, but the idle has to be all the way up, the problem isn't the switch box.
Where did you adjust the idle all the way up?
What is your motors serial number so I can bring up any diagrams we may need?
This is likely a fuel delivery problem, probably a plugged up carb or two, but it could also be a fuel pump issue though that is not as likely.
Have you checked for spark on each cylinder? I am sorry, I assumed you had when you changed plugs. I should have asked.
If you haven't, you need to do so. We need to know if each cylinder is getting a good spark.
Did the motor end up running correctly? Was this just a start up issue, after witch the motor ran ok?
If it was, tell me what you did when you started the motor. What was your start up procedure?
Yep, this is a fuel issue.
Have you tried priming the motor with the primer bulb prior to starting? I know you should only have to do that on the first start up of the day, but trying it can help us get the problem narrowed down.
You can also try squeezing the primer (well, having a helper do it) while trying to accelerate to see if this allows you more get up and go.
You may be having a problem with the fuel draining back into the fuel tank when you shut down the motor, but I think you might need to rebuild the fuel pump on the side of the motor.