The Lifetime Learning Credit is also limited to tax liability. So, the credit can reduce your tax liability to zero, but it can't give you an additional credit beyond your tax liability. (This is unlike the American Opportunity Credit where you can receive an additional refund from your credit after its applied to your tax liability).
So, its likely that $710 is your tax liability at the point of when your educational credit is applied and that is why your credit is only showing as $710. A couple other things to note would be (1) to make sure you properly entered the additional payment and (2) your education expenses paid must be reduced by any scholarships or grants received. These are also reasons it could be less but it is likely you tax liability limitation.
