Cant recover password, No serial number.
Write a support ticket. It may take some questions and answers, but they are still able to solve your problems.
ArenaNet Communications Manager
As I just wrote in another thread, You should contact Support by filing a ticket through the “Ask a Question” tab on that linked page. They will be able to assist you using other means to establish that you are the owner of the account. Naturally, this is important from a security standpoint, so you will be asked to provide different information, as explained in this post.
Gaile Gray
Communications Manager
Guild & Fansite Relations; In-Game Events
ArenaNet
Communications Manager
Guild & Fansite Relations; In-Game Events
ArenaNet