On the Home page after you log in to MyVerizon, on the right side is a box that says My Bill - with [ayment information and amounts. To the right of My Bill it says Account followed by a number - that's your account number.
If you are on a pre-paid account, your account number is your phone number.
If following the steps already given in this thread do not work, then perhaps visiting a store and asking CS there will work for you. Are you a secondary line on a family plan? That may be why the account number isn't showing on the page.