Ask a Business Lawyer. Get Business Law Questions Answered ASAP.
You can not do business in the name of a non-existent corporate entity. You would need to convey the website to the new entity before you close the old one and then adopt the name as a DBA of the new entity.
If your corporation does not exist then you can use its website and do business under its name unless you file for a DBA in the name of the old corp/website.
Otherwise, you are not maintaining the separate identity of both corporations and could lose the shield from personal liability.
Is that more clear?
Did you have further questions? Have I answered your question?
Are you still with me?