Did you try doing a password reset on your parent's webmail account? I was able to do that to my mother's Yahoo account after she died (since she had set up her security questions with truthful answers), and I was then able to do the same for her Facebook account, which was tied to that email.
Granted, I had to actually ask one of my aunts for the answer to one of the questions, since it was about something we had never discussed, but overall it wasn't too difficult.
It was actually kind of humorous, since my mother always made a fuss about making me turn around when she would enter her password, and I would tell her that she was being silly, and that if I *really* wanted to get into her account, I could. Heh, I still get the mental image of the look on her face she would always get whenever something happened that enabled me to tell her "I told you so!".