I was given a state tax credit that I don't qualify for and now I can't file my state taxes online, after I already paid for it. Can I start my state tax forms over?

Yes, you can.  To remove and re-enter state information in TurboTax Online: 

1. Open TurboTax Online
2. Select  Tax Home in the left pane
3. Select the dropdown to the right of State Taxes
4. Select  Pick up where you left off
5. In the left pane, select the dropdown to the right of State Taxes, if it's not already open
6. Select Your State Returns
7. On the Status of your state returns screen, select the trashcan to the right of your state
8. In the popup, select Delete
9. To start entering your state information again, select Add another State on the Status of your state returns screen
10. Select your state, and enter all appropriate information 

If the TurboTax Online navigation described above doesn't look like what you're seeing, see the TurboTax Help article Why does the TurboTax navigation menu look different for me?.