Starter won't totally engage on my 2002 Yamaha Vstar 1000.

need a clymer/haynes manual or similar--u may just hav a corroded connection or a bad relay--other makes have similar books

If the starter relay is working properly after you install the fully charged battery, and that means engaging when you hit the button, then there's no reason to replace it. Unless you just want to replace it with something better.

The one way clutch that engages the starter motor to the flywheel is chattered or damaged and needs to be replaced. The starter motor turns a small gear that is connected to a large gear by a small chain. On the side of the big gear is a smooth machined surface that the one way clutch grabs when the starter is engaged. The surface is chattered and the three grabber rollers wont jam or grab on the surface unless it is smooth therefore the starter spins but the motor does not. You will probably have to replace the large gear and possibly the three rollers also.

The starter button is used in an open circuit design.
You must press the starter button to "Close" this circuit before the starter will engage. Taking the starter button out of the loop helps support the suspect short. Assuming you kept the starter button wires from touching. :) If not, it is most likely the starter button.

Trace the wires coming from the starter button.
There could be a short circuit. (Same as pushing the starter button). Check along the handle bars and anywhere rubbing could cause a break in the insulation. Try this at night with the lights off.
You may be able to SEE the spark and locate it quickly.

Good luck!

Twisted bolts on the starter are never a good thing. There is also a one-way starter clutch on the crank behind the flywheel that can be damaged. If it engages intermittently, it's on its way out. Both the starter and starter clutch are prone to failure on VStars... and neither are cheap to fix. Hopefully your bike is still under warranty.