How can I be refunded for my $39.99 state fee if I am unable to file through turbotax?

Are you using the Online version?  The online fees are to prepare the return whether you efile or print and mail.  

Or are you using the CD/Download Desktop program?

Started on phone app then tried on ipad (app and browsers) and two separate computers (two separate browsers on each). I could get to the efile part then it said there was an issue to fix. I needed to uncheck a bubble. In none of those places could I get the bubble to uncheck. Other bubbles and selections would change but that one no. Finally used a different software (that I had used in past years) to file.