1. Buy a windows dedicated server, you can get a basic one from
volumedrive for $55 per month. This will allow you to keep using your existing account and services (gmail, blogspot, youtube etc) without running the risk of having your new account linked to it if you forget to clear your cookies or something.
2. Login to your dedicated server via remote desktop and create a new google account, don't login to this account from anywhere else and don't use any other google accounts on this server.
3. Get a new credit card, call your bank and tell them you lost it or some other lame excuse so they give you a new number or apply for another.
4. Signup for adwords with your new card, thanks to the
address verification system you can use a fake name and a fake street name and your credit card will still work.
For example if this is your billing info:
John Doe
1452 Palm Street
New York, NY
58201
You could enter this, and it will still work:
Jack Smith
1452 Clover Drive
San Diego, CA
58201
Anything that isn't in
bold can be changed to whatever you want
That will be $197 please, but if you act in the next 15 minutes you'll only have to pay $4.97, even if it's 3 AM!