Small Engines (Lawn Mowers, etc.): Craftsman mower, hp motor, voltage drop

Question
QUESTION: I have a model 917.271631 with a 16 1/2 hp motor and I replaced the battery and it ran fine, a week later it will not start and I am getting 9 volts to the starter and 12 to the solenoid, is this correct or is the solenoid bad?  How do I check that the alternator is charging the battery?  Thanks

ANSWER: Well if you are reading these voltages, then you must have a voltmeter, and that would be all that you need.

But when you try to start, is the starter engaging/trying to turn the engine over?
Or nothing at all?

If you can jump it and get it running again, take a reading at the
battery, and it should read over 13 plus volts, more like 14.

   Double check your connections too, let me know what you find.

---------- FOLLOW-UP ----------

QUESTION: I haven't tried to jump start it yet, I do have almost 13 volts on the battery but I did have more when I first installed the battery a week ago.  I think it is not charging the battery or the solenoid is bad.  How do I check these?  Thanks

Answer
With that high of a reading, the battery is fine, you read a pretty big voltage drop across the solenoid, so it may be bad.  The
craftsman mowers have a solenoid that have two small terminals,
which make diagnostics a bit harder.
   Crossing the two large terminals should produce sparks and the starter should crank the engine, if not then you have something else going on.
  When you turn the key, nothing happens???

If it tries to start, but struggles to turn the engine over, then you should adjust your engine's valves.

Let me know what you find.