My Macbook is being a huge PITA. It's about 6 years old and lately it's been taking a really long time to shut down and turn on (sometimes several minutes). It doesn't ALWAYS take that long, but 9 times out of 10. I deleted any unnecessary files and applications and emptied the trash. It helped a little but it's still pretty slow. Everything else runs normal speed.
Recently it started shutting down randomly. Not like going through full shut down, but just turning off. It happened after I was watching a TV show on a website. I deleted all my cookies, and am staying away from the website, but it did it again.
Any suggestions for either issue?
I should add that I plan to call and make an appointment with the Genius Bar but the nearest Apple store is over an hour away so I was hoping for some ideas first.

Everything the light touches is my kingdom.