Lawnmower Advice

Help! My Self Propelled Lawnmower is an absolute bear to start. What is the problem?
I have a 5 yr old Sears Craftsman, model #917-377690 (22 inch, 6/75 HP Eager 1). It has always started rough, but this Spring has been really bad. It starts just fine but after about 5 seconds it just dies out. It usually will start (and stay running) after about 10 attempts (yesterday it was 20!).I suspect it is a fuel line issue (clog?, bad pump?). Is there a choke on this mower? (I could not see one). I did a full tune-up but this did not help. I have used fuel stabilizer & a new sparkplug and air filter. I would appreciate any advice.
You can’t replace just the plug wire, the whole coil has to be replaced and they rarely go bad…. its not a spark problem at all, its fuel related…. it also doesn’t have a fuel pump… its gravity fed. Take the fuel line off at the carb while pinching it, let it go and watch for a good flow…. if thats not good… replace the inline fuel filter if you have one, or clean the intank filter(just a mesh screen at the fuel outlet) and try it without the gascap first though… if it runs good…. replace it…. otherwise its just to rule it out. Then I’d move on to trash in the carb… you say you used stabilizer, so I hopefully can rule out bad gas, and the carbs gummed. Take the fuel bowl off (cut the fuel off first) and spray it out good with the straw on your can of carb cleaner, even up the hole the bolt went to hold the bowl on, through any and all holes…. this MAY get you going most of the time…. if not a carb rebuild (soak for a few hours in carb cleaner and blown out and rebuilt using a carb kit) is in order. Also make sure the float isn’t sticking.