If I received a form 1098-T but dropped all of my classes and returned the money, do I have to enter the form on my taxes?

No, you are not required to report your education expenses.  

No. 

The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income. 

If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)

You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T.