I've been trying to get EA Help to change my email to a new one (I can't access the previous one), for 2 months now, and they keep closing my case without considering it. There is only so much patience I have for inefficiency this bad. Now I'm turning to Answers HQ in hopes that SOMEONE would be able to help.
Unfortunately an email change is not something that we can help with here on Answers HQ. Since you cannot currently access the email address on your account you'll need to reach out to the Account Recovery team so they can help you get it updated.
When you have a chance please fill out the Account Recovery form over at the EA Help site. That will create a case so the Account Recovery team can verify the account with you and help you update that email. Keep an eye out for a response at the active email you provide when you fill out the form.