If you're having trouble with your start button, it may be because it needs to be cleaned. Over time an oxide layer will build up on the contacts and it will cause problems from intermittent op to no op.
Start by taking out the 2 screws that hold the right side handlebar control together shown in the picture.
The control can now be split. There are no loose parts to fall out at this point.
The contact is shown by the upper arrow. The screw shown by the lower arrow must first be removed. Once the screw is removed, you need to keep track of things as this is where the small parts ans a spring will get away from you.
The screw has been removed and you can see the back of the contact better here. There is a spring under the contact so be careful not to lose it. Don't be working in the grass as if you drop it there you're going to be up a creek.