If you received a Notice to File a Business Property Statement from the Assessor and your business is no longer in operation, you are still required to file the Business Property Statement. You should also include a note on the Business Property Statement indicating that the business has closed, so the Assessor does not continue to assess the property.
The articles of organization also should include information about how your LLC will be managed. You need to indicate whether the members of the LLC will do hands-on management or if there will be hired management. Another requirement is to discuss how long the LLC will be in existence (there is no limit on this, so it is fine to say in perpetuity).
Where the equipment you use in your business was acquired as a gift, you may report your estimate of its current market value on the Business Property Statement (that is, what you think it would sell for in the open market place). Enter that estimated value in the most current year's cost line and add a note indicating that the entry is an estimate.