Don't even know how to describe this... Please tell me whats wrong!

Question

Yesterday, my Macbook shut off because of no power. I turned it back on about 20 mins later and my clock was wrong. I opened it and had to manually change the time from Dec 31, 2000 7 pm to current date and time. Next I noticed that Safari and FireFox were acting me for verification all the time on webpages. The biggest problem is that my Coursesmart app showed that one of my books was expired on 7-17-11, which isn't here yet. I tried to go to the website through the app and it said the certificate was not valid and that the website i was trying to go to might be fake. I talked to coursesmart up to the top techs, did some things with the computer like uninstall, update, keys,. they couldn't figure it out. I figured out that all of my certificates for anything are gone. I went through the key and found the area that says what my certificates are. Its like my computer has gone back and lost all of its information. Some websites are not working, passwords are not working, and its lagging sometimes. I can't timewarp my computer because it was never turned on. Please tell me whats wrong!

Answer 1

The abnormal shutdown most likely resulted in corrupted files. Start with this:
Repair the Hard Drive and Permissions
Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
If this doesn't work (probably won't) then backup your files and reinstall OS X. The SL installer will not erase the drive but will install a new copy of OS X then transfer all your files and applications into the new system.