Small Engines (Lawn Mowers, etc.): Engine wont start, mtd mower, safety switches

Question
My mtd mower model 13a6673g118 will not start.I replaced the carburetor a few years ago and it has been great for two years.  About a month ago I started to have trouble starting it.  It would take longer and longer to start it.  I had the battery tested and it was fine.  I put in a new spark plug and it started immediately but then next time nothing and it has been dead for two weeks.  My original thought was the solenoid and safety switches but when I tested the spark plug, I had a blue spark.  Does that mean the issue is not electrical and something within the engine?  If so, what should my next step be?

Answer
If you have spark, it's probably a fuel problem. Without more detailed information, I can't give you much more than that. Does it feel like it has compression? Does it spin freely? When you say it took longer and longer to start it, it sounds like a carburetor problem or possibly compression. What kind of engine? Is the spark plug getting wet? These are all valuable pieces of information for correct diagnosis.