You say the problem is with visiting web sites but you never say if you are using a web browser or some type of FTP program.
If you are using a web browser, you never say which one you are using.
You mention Mozilla, which suggests you may be using the Firefox web browser but you never say what the version number is.
If you are using a fairly current version of Firefox, it does have the option of letting the user add a master password to protect the saved user names and passwords for web sites. You have to enter the master password before being able to access the protected list.