Battery Not Charging

Hi guys!
I have a 2010 FZ1 and I'm having a problem with the battery not having enough juice to start the bike. It runs fine once it's started but I can only start it while it's on the battery tender. If I take it off even for a few minutes and then try to start it, it chugs and fails to start. I bought a new battery but still have the same problem. My understanding is that the problem is likely with my stator or my rectifier. How can I can figure out which, if either, is the problem? Is this a repair I can do myself? I have a multimeter and decent socket it set but that's about it.

Thanks!
 
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