An SMC reset might help, but doesn't sound like a power problem to me. I'd make sure the machine is OFF first thing by holding power button down for 5+ seconds. Then try resetting PRAM: Press power button momentarily and IMMEDIATELY press and hold Command+Option+P+R keys until you hear startup tone 3 times. If that doesn't do it (and SMC reset doesn't work), c'mon back and we'll try something else.
Hope it's problem solved.