Small Engines (Lawn Mowers, etc.): Tecumseh 5.5HP Cold Start, spark plug wire, power of positive thinking

Question
12+ year old trusty Ariens/Tecumseh combo on mower now takes many, many, many pulls to start from cold. Once run for a short while, can stop and will start back up easily on one pull. New spark plug + air filter seemed to help for a couple cold starts (maybe coinsidence or power of positive thinking), but now back to multi-pulls. Noted the rubber on the tip of spark plug wire's socket looks like it burned through at some point (1/8" diam. hole at very top of plug), but the wire itself seems to still be making good contact. Can/should this wire be changed? If so, where's the best place to look for such small engine parts? Any suggestions/best guesses would be appreciated. Thanks.

Answer
Hi Kevin,

Since the problem is only on cold starts, I suspect the choke or a lack of fuel due to a fuel leak.  Is there a primer bulb?  Look into the carb throat to see if the choke plate is closing when the choke is on.  Is the bowl wet or any sign of a leak?

Let me know what you find.
Michael