Small Engines (Lawn Mowers, etc.): Dixon ZTR 304 Lawn Mower Wont Start, loose ground, behavoir

Question
My lawn mower will not start. I only get an occasional click. I have replaced the solenoid. Jumpering across the solenoid to the exciter cable does not work. I never get 12 volts on the other side of the solenoid even if I disconnect the starter. When I disconnect the exciter cable from the solenoid and measure the voltage on the cable when I turn the ignition, I get 12+ volts. When the cable is attached to the solenoid and I turn the ignition, it never goes above 1 volt. This is the same behavoir that I saw before I replaced the solenoid. I am so confused.

It is a 3 post solenoid. 1st big post is to the battery and a smaller cable going towards the starter. The 2nd big post goes to the starter. The small post "seems" to go over to the ignition switch but it is hard to tell. There are also two small cables attached to the bolts holding the solenoid in place.

MY suspicion is a bad battery or a loose ground? Am I on the right track?

Answer
Hi Scott,

I'm sorry for my delay.

Yes, I suspect a weak battery or it's connections.  
Test the battery by jumping it to the starter.  If it cranks the starter, then it is good.  If not, replace the
battery.  

Let me know how you make out.
Michael