I didn't recieve a 1098T in the mail but I see it online. It says ineligible payment, paid by financial aid. What does that mean?

You will need to call the school to clarify. It sounds like your tuition was paid through some form of financial aid.

That's a new one. It must be something your school does on it's own. You'll have to ask them. It's not an IRS requirement.  

"Paid by financial aid" does not preclude you, or your parents, from claiming a tuition credit or deduction. Student aid may include loans as well as scholarships.  Loans are definitely eligible for a tax credit. Grants may be, depending on the conditions of the grant.  On the other hand, if this is your school's way of saying it was a condition of your grant that it be used to pay tuition, then they are right, you are ineligible.