Do check that fuel line first. It's amazing many problems are due to the simplest of causes. It's a cheap and easy fix. Even if the outside of the line looks OK, it may be cracked on the inside, especially if the bike has been sitting for a while. You should also look at replacing cork bowl gaskets while you're at it.
By the time you're done you will be an expert at popping the bales, pulling off the bowls and replacing them without tools and without spilling a drop of gas.
Good luck with your fix!
John