Shut down / Wake up Issues

My laptop shuts down when it is unplugged. Even when I have put it to sleep while plugged in, the next time I open my laptop it does not wake up from sleep no matter the combination or number of keys I hit. I have to hit the power button. Sometimes after hitting the power button I get the grey screen and ten bars restarting what was open. Other times, even with a short press, I end up having hard turned it on. That is, my computer DOES turn on when unplugged, so I do not believe it is a battery issue, like everyone else's problems. The battery has 247 cycles, if you were curious. I have reset the SMC as well.

Because MS Word Autorecover is poor, I actually lost my senior dissertation because of this problem. So, I would really appreciate any tips or ideas or brainstorming from ya'll. Love!