trouble starting sometimes. solenoid??connection?? starter??

It seems like the starter isn't getting enough power. Had the battery tested & its fine. When running the voltage meter wouldn't go above 12.89 even at high rpms. When it does have trouble starting the starter makes a buzzing noise like a car does when the battery going dead. And sometimes the start button won't do anything when I push it. Other times its fine. This seemed to just start doing this after I removed the stock air box. I had to remove the starter to get the air box out. I also moved the battery. I wonder if there is a bad connection somewhere. It will sometimes turn over and just not start. But if I jump it off a car battery it starts right up. It starts fine most of the day and then BAM!!! For no reason I can see, it just won't start. Rrrrrr I just don't know where to start looking. Please help.

 

You might want to pull the S motor, clean out it & check the length of the brushes.

 

Thanks wizard that's a great idea. I didn't think about that.