Do I need to file a Utah State tax return if I didn't earn money while I lived in the state of Utah, but received a pell grant for school while living in that state?

Yes, you do.  A part-year resident is a person who is a Utah resident for part of the year and a nonresident for part of the year. All income received during the period of Utah residency is taxable in Utah, regardless of where that income is earned, unless specifically exempted. Income from Utah sources is taxable in Utah during the period of nonresidency.