Bill I've never seen one of these Shineray's. But it sounds like the 110 engine thats in the quad I have under the Ducar name I've seen them in alot of china built quads. This site here is another brand of quad with this 110 engine in it http://www.atvforless.com/LM110.htm
Check the specs out and see if it's the same. Below the specs they have a parts list with prices. The starter I think is $75 bucks Canadian so about $65 US. They also list a parts manual and service manual on there too.
Before you start pulling things apart did you check to see the battery and connections are good?? Try boosting it with a good battery and see if it turns over.
MY 1985 Honda TRX 250 would do the same thing, sometimes it was the battery. But most of the time it was the Brushes in the starter. I've probably replaced those 2 brushes 4-5times over the years at 30 bucks a pop from Honda. A starter was like $300-400 for it!!! Maybe now a days you can buy them aftermarket for half the cash?? Good old quad just has a weak starter design.