I have about 250,000 emails, wondering on how to monetize?

[Jake]

If Aweber has not records from your prior account, that list will be treated as a complete unknown, and will require you to get people to sign up again through the double opt-in process, they probably also will require you to do it in smaller batches. You really did sacrifice a significant amount of value when you let the account lapse.
You do know these emails are interested in your field, the list is are more valuable than randomly scraped addresses (I recall one underground service offering 1 Billion email addresses)
Lists in profitable fields can sell for more than 50 cents an address, some marketers have no problem spending $5 a head to compile a list of the right prospects, knowing it will pay off within a year.

I would think you might mention the old site to trigger recognition, and give a new domain name you had switch over to as the reason for the double opt-in.

I would not risk can-spam penalties for marketing to that list without it being sanitized by some email manager like Aweber.