If you didn't get disks with the eMac, or you would prefer to take your chances with the hard drive as it is - do you know the present password?
You can open your system preferences/Accounts pane, and add a new account. Make sure to select the block to allow the user to administer the computer. When the new account is created - log out of your user, and choose your new user from the list. Enter your new password there, and you will login to your new user account. Go in to that same system preferences/Accounts pane, and click on the _old_ account, and click the minus (-) at the bottom of the accounts window to delete the old account. And, you're done, with a brand-new account (on top of an old operating system that you're not completely sure about - eh?) But, it's your choice then....