Few of my applications start I have a Macbook Pro 15 inch 2009 running OS X 10.10.2. I want to update the OS to El Capitan but the App Store won't open - nor will Safari, Contact, Calendars etc.
Chrome seems to be one of a handful of the apps that are opening fortunately. 

I've already tried the following:

1 - Opened Library/Preferences/com.apple.appstore.plist and deleted it

2 - As above but for Safari because apparently Safari, App Store and iTunes share the same history and preferences?

3 - Created another user but encountered the exact same problem.

4 - Tried running this command on iTerm (because Terminal wouldn't run either)

softwareupdate -a -i


but this failed because I don't have the correct permissions. On this one I was logged in as an Admin and also tried starting a bash command with sudo -s but it didn't output anything.

5 - I attempted to start Mac OS Recovery but holding cmd+r on startup but it's asking for a password but none of the passwords for any of the admin accounts work.

What else can I possibly try short of ordering recovery disks or saying screw it and buying a new Macbook altogether (which I really don't want to do!)

Thanks
When you restart a Mac holding command R or just option to choose a different os, that indicates a firmware password lock is present.


https://support.apple.com/en-us/HT204455
https://support.apple.com/en-us/HT203409


After reading the above, you might need a repair to regain control to wipe and reinstall or just boot to a working OS. Since your Mac is outside normal support by Apple, you might need to change the hardware yourself - perhaps removing one RAM stick per these threads:


How do Apple engineers reset EFI password on new MacBooks?
https://apple.stackexchange.com/a/121801/5472


Once that's done, you can boot to Recovery HD and reinstall the OS or erase the drive as needed.