Hello. Welcome to JustAnswer, a paid global technical support site.
I would like to start off saying that I am not a representative of Google. I am just giving you a straight answer as an IT professional.
I understand the methods you have taken to recover your account. I want to make sure that all avenues are covered. If you have exhausted these options, it is highly unlikely you will ever recover your account.
Please go to the forgot my password page (https://www.google.com/accounts/ForgotPasswd).
If that option doesn't work, you can trying the cannot access my account page (https://www.google.com/support/accounts/bin/request.py?ara=1&hl=en&contact_type=ara&ctx=ara)
If you can get through and change your password, I would suggest using a password XXXXX at least 10-20 characters, with a mixture of UPPERCASE, lowercase, and numbers (1234), preferably alternating (i.e. M1y2p3A4s5S6w7O8r9D). Also make your security questions very difficult to answer. Don't use something as common as mother's maiden name or first child's name. Make the answer very difficult, and I would even suggest throwing in a sequence of numbers at the end of the answer to make it harder for the hacker.
Also, before you log in, look at the address bar of your browser to make sure you are on the right site to log in. (i.e. make sure your address bar says https://www.google.com and not something like http:// 123abc. randomurl.com/ www.google.com/). A lot of phishers/hackers have been using the tactic of making a page look exactly like your log on page to trick you into typing your password.
If in doubt, type in the base URL yourself (i.e. http://www.google.com) in the browser.
If you still cannot get through or the hacker has modified your security questions/answers, and you have no credit card information or billing information on record, you have no way to verify your account, thus this is nothing you can do.
I have seen some people that have had success with calling (NNN) NNN-NNNN (press 0 when prompted for extension). There are some people who have not.
The only thing that can really save you is if you used Google Checkout to purchase something and can verify that billing information, but that may be a slim chance as well.
Unfortunately, Google's live support is almost non-existent.
The problem with free e-mail services is that they rely on security question/answer combinations for verification. If you forget these and/or your account is hacked and a hacker changes the info, you have no way to verify your account. With paid e-mail services, you can easily verify your identity by verifying your billing information.
If you have tried all these methods without success, you will need to accept that your account will not be recovered and move forward.
In the future, my suggestion would be to invest in a paid email account service so that you can always verify your billing information in case something like this happens.
Let me know if you have any questions or comments by replying to this thread. I am here to assist you! Good luck.