Already have a INC. but I'm starting a new unrelated business, do I need to incorporate again?

Maybe an attorney or accountant can correct me, but I think that it doesn't matter which you do.

Running a second LLC will mean that you have to do all of the same reporting to the IRS and local government twice, have to keep two sets of books, etc.

Making it a division of your existing company means that you will have more complicated accounting if you want to track the profitability of both ventures.

In the end, it just matters what makes more sense to you. I don't think there are any legal requirements either way, but I want be sure to say I am neither and attorney nor a CPA. Just a guy who has started a few companies.

Yes, you can run the new business under your existing corporation (assuming there is nothing in the articles of incorporation that precludes the new business).

Whether you should do so is a business / accounting / tax, rather than legal, issue.

Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.

From llcsexplained.com (a great resource that I have no connection to):

Without holding each business interest in a separate LLC, in a worst-case scenario the entrepreneur may lose all three of his businesses if something bad happens to any one of the businesses.

Note that I'm not a lawyer, and this is not legal advise.