Remote management of parents' computers [duplicate]

TeamViewer is THE way to go in my opinion. You would install the Full version, set it to start with Windows, and set a specific password. After you have it setup, and have the 9-digit code, it will work EXACTLY as you described you wanted.

http://www.teamviewer.com/en/index.aspx

You go into the Extras>Options>General to set it to start with Windows:

And you go into the Extras>Options>Security to set the password:

I use LogMeIn to be able to log into my family computers. It's really simple. Just log into logmein.com from the computer you want to control, and then just add the computer. You will then have a list of computers that you can log into. LogMeIn is free for personal use, with optional paid plans.