Can my laptop turn itself on after I've shut it down?
At one time, I used to run a couple applications that would inhibit my iMac from going to sleep.  So, if you have something running in the background that stops your mac from sleeping, that would be a candidate.  If it woke up, you may have a backup while plugged in turned on.  That does wake the Mac while it does that trick.

Now as for frying your HD?  Well, who knows.  Fried HDs do happen, and I suppose it could happen while a laptop is shutting down, which would answer both questions.  I did recently replace a HD on an older laptop.