If you contact support from your account, the support reply may probably go to an email you don't have access to.
Log out of the Spotify website in your browser and fill out this contact form. Someone from Spotify will be happy to help you out.
Make sure you are logged out of any Spotify account in your browser when using the contact form or the username and custom email field will not show up. It is important so that you can enter the information of the account you are having trouble with. If you are logged in with a different account that is not having the problem, that account info will be used and support will be confused.
You should get a reply within 24-48 hours. Don't forget to check your spam folder for responses as they may end up there.
If you get an automated email directing you to the community or help pages, you need to reply directly to that email (even if its from no-reply) and one of the customer services agents will get back to you.
When you are on the page to close the account there's not the usual confirmation / 'send" tab to but it will still close the account. A follow up email may take 2 to three days. I know that it appears confusing but it will close your account.