Nope. You need to open a new business. You specifically stated "venture was complete" for the now closed down company. So for a new venture or whatever, you need a new company.

While you don't need to do anything at the federal level, you do need to contact your Secretary of State and understand what the "old" LLC needs to file to unregister that LLC.  

Your facts don't indicate what state, but some states require annual reporting and / or fees to the Secretary of State.  These reports / fees will be required to continue for the "old" LLC until you unregister the entity; these are sometimes called articles of dissolution or something along those lines.