Battery??

My 2007 MacBook Pro has about a 2 year old battery. If I have it charged to 100% and disconnect the power cord for no more than an hour, the computer will not start. If I plug it back in it will start and say the battery is at 0% charge. iStat Pro says 214 cycles, 72% health and 0% charge. So the question is whether or not this is the battery or something else? Power supply? Any ideas are welcome.