Log on issue due to closed e-mail account

If you had access to the associated email, you could attempt a password reset. This would send a reset link to the email if the Dropbox account still exists.

However, since you don't have access to the email, this option isn't available to you. Additionally, it's worth noting that Dropbox accounts left idle for more than a year are often deleted due to inactivity, as per my information.
Regrettably, without access to the email, regaining access to the Dropbox account is not possible.

You might consider contacting the email service provider to see if they can reinstate your email address, even temporarily.

You can either use or sign up for a new email with the same ID as your old email. If this option is available, the reset password will be sent to the email address.