Mountain Lion lockscreen when trying other startup options

That sounds like you are encountering a firmware password. Without that password, you cannot reinstall the system, among other things. If you don't know that password for whatever reason, you will need to take the machine to Apple for assistance. For security reasons, there is no other way to reset a firmware password.

If it was bought second-hand, the previous owner set a firmware password. If you can still contact the seller, try asking for the password. If not, the Apple Store is the only option.

The firmware password is only involved in certain limited actions, such as booting from another drive. See:

http://support.apple.com/kb/HT1352

Exhibiton wrote:

If this is the case, shouldnt it have asked that password before also? This is the first time in a year it asked for it.

Was your Air bought Used?

Was your Air bought Used?

One of his messages said that it was, though oddly, I notice that that part of the message has been changed.

You can install systems like Lion and Mountain Lion without rebooting from a separate disk, just by running the installer. I would guess that this would not involve the firmware password (though I'm not sure, as that install method is relatively new and not mentioned in Apple's documentation of firmware passwords).

However, if you have done clean installs on that machine at any point, booting from an install disk or into recovery mode, then I would think the firmware password must have been added at some later date.

Then the password was added somehow after the last clean install. Regardless of how it happened, though, the screen that you took a picture of is a firmware password screen.

I'm not actually sure... you'll probably want to call them in advance to find out. If not, I guess try calling Apple's tech support for advice.