If it's the one in the image below it's not worth fixing as the starters always break..
I would make sure the plug is good remove the air filter cover and start the trimmer and when it starts to cut out spray some fuel or starter fluid into the carby and if it still dies you know it's the coil.
Usually the fuel hoses need replacing if they haven't been done for a while as you can get very minor air leaks and the fuel filter could be blocked ,occasionally the primer bubble needs replacing even though it looks ok.
I mostly can't even give them away for free when they work well because everyone here have good trimmers and don't want old 2 stroke trimmers,they have Honda or battery operated trimmers these days.
Mower shops were charging $120.. for a trimmer service 5 years ago.
