I bought a MacBook Pro with Lion secondhand. I've had some start-up problems (hangs every other time approx.) which are manageable, but now I can't unlock System Preferences etc to make essential changes, or install new apps, using the user name I inherited. The password is blank. I can set one - and change it back to blank again, but it makes no difference - I can't unlock the padlock.

This is a new problem - to begin with I did install software without difficulty. But I can't now.

I have found suggested fixes to the 'lock' problem involving changing admin/user names - but I'm new to the Mac and confused by the hierachy of names within an account: root, administrator, user, long name, short name, keychain, Apple ID, etc. (On a PC I just had administrator and user!) Can someone explain all these in simple terms and how they are related?

I would like to change the old user/admin names etc to the simplest arrangement, with passwords, in keeping with my sole user status. Is this possible without compromising any of the software I have installed (and, ideally, that which I inherited already loaded).

Thanks in advance.