I am travelling around Australia and after a few weeks after I arrived my macbook pro wouldn't turn on with out it being plugged into the mains.

(which really defeats the object of being a laptop) First I thought it might have been a heat issue with it being 100 degree's outside but even when the temperature has dropped to what it is used to back home is still won't power up. The battery is fully charged but when pressing the power button it only shows one light as it try’s to boot up. When you press the battery check it come up with all lights. Anyone have any suggestions? Can I take it to apple even if imp in another country?