Have you tried the following when requesting your access code?
Add "noreply@mail.elderscrollsonline.com" to your email account's list of approved e-mail senders.
Check your spam or junk mail folders.
If you are using Gmail with the Inbox categories feature, also check your Social folder.
If you are using a firewall or anti-virus, temporarily disable them before requesting a new code.
If you have not received your access code after trying the steps above, you should contact customer support to request an email address change by selecting "No Longer Have Access / Can't Remember Email on Account" in the Issue Type field on this form.