lets start with the easy stuff. i have to agree with stayscool....your winch, headlights ect all run off of volts, but actually starting the machine takes amps. you battery can have full volts, and no amps and cause an identical problem to this. its very misleading...a battery charger can say your battery is fully charged, but it wont start the machine. all a battery charger shows it volts, not amps.
here is a link to a write up i did at this forum. it might be worth your time to read. the only way to find out for sure it to have a load test performed on the battery. basically a machine will draw a large amount of amps from the battery and see how well it supplies and recovers from the amp draw. its quick (15 seconds) and easy, and will either confirm or dismiss the battery has the culprit. Preventative Battery Maintence