What if my parent is claiming me as a dependent, but not claiming the education expenses on their tax return, can I claim it on my return?

[MinhT1]

No.

If you are a dependent of your parents, then only your parents can claim your education expenses and your form 1098-T must be entered on their return.

If you can't be claimed as a dependent, then you enter your 1098-T form on your own return.

It doesn't matter who paid your tuition.

The following is an extract of an IRS document:

Who can claim a dependent's education expenses.   If a student is claimed as a dependent on another person's tax return, all qualified education expenses of the student are treated as having been paid by that person. Therefore, only that person can claim an education credit for the student. If a student is not claimed as a dependent on another person's tax return, only the student can claim a credit.

Please also read this TurboTax article on Who can I claim as a Tax Dependent.