For the starter motor issue, with a Known Good battery, do you hear a fairly distinct "click" when you hit the starter button? If you don't then it's probably the relay, which is like a 50 cent part--they're so cheap you have to buy them in like ten packs on Amazon. It might also be that the wiring for the relay from the switch is damaged.
You can also check the motor by bypassing the switch. Get a piece of electrical wire--an old lamp cord you don't mind cutting and stripping the ends will do fine--and touching one end to the positive terminal of the battery and the other to the positive terminal on the motor (it'll be the one with a heavy gauge wire attached). If it spins, you're good and you're back to the relay or wiring.
To check the relay, you can do the same test with your lamp cord. Touch the battery to to the relay's trigger pin and if it starts, it's the wiring. If not, it's the relay.
If it's a DR, when you remove the cylinder shroud and flywheel cover, you'll see a small "DR" on the side at the base of the cylinder. You'll also see a couple of cooling fins have been ground off to create clearance for the starter ring on the flywheel.