MacBook Air not functioning properly

Hi all, my MacBook Air (running on Lion OS X while downloading Mavericks, purchased in 2012) is not functioning properly. Over the summer I tend to not use my laptop a lot since I mainly use it for schoolwork. I had opened my Air for the first time in a while and it was fine - however after that I had left the screen open and the screen went dark. I had left my Air open for a few weeks and when I tried to turn it on, it would not do anything. It would not respond to anything I did and eventually had to restart my computer in SafeMode. I thought I had fixed my problems however a few applications were giving me trouble

iPhoto would not open at all and after many failed attempts to debug my issues, I had to delete the application from my computer entirely. Eventually I tried to redownload it from the appstore but it wouldn't work so I gave up.

Recently, I noticed that my Mail application will not open (even though the system preferences for it will). I also noticed that a few of my System Preferences will not open - Energy Saver, Desktop & Screen Saver, and Spotlight.

I am currently downloading the newest update, Mavericks. I did download Mountain Lion, however when I rebooted my laptop over the summer in Safe Mode I must have reverted back to a back up that did not have Mountain Lion downloaded into my computer.

I am at a loss of what to do.