First, summer camp is eligible if it is a day camp, and one of the reasons you send your child is so the child can be cared for while you (and your spouse if married) can work. Overnight camp is not eligible.
Second, you can't take the credit and the FSA, which is why the program tells you that you don't get a credit. If you paid (for example) $2400 for qualifying care, and had a $2000 FSA, the remaining $400 could be applied toward the credit. Since your care was less than your FSA, you aren't eligible for any credit.
Lastly, if you withdrew the money from the FSA, but spent it on non-qualified care, you must still fill out that section in Turbotax. Turbotax will calculate that the reimbursement is not eligible to be tax-free and will add it back to your taxable income (but there is no penalty.). I don't quite know how that would be entered in Turbotax, but you would indicate at some point that you had no qualified expenses. (First, however, you should be asked if you forfeited any money in the account, since you forfeited $74, that amount is not taxable, it is just lost.). After being asked about the forfeit, you should be asked if you paid for qualifying care and you would say no. The $1926 would be added to your taxable income.
However, you can attempt to claim the credit without an EIN if you want to file by mail. You would need to use a fake EIN to pass the interview, you can try 999-88-9999. Print your return instead of e-filing. Cover the fake EIN with white-out. Attach a written statement giving the name, address and phone number of the provider, and provide an explanation of your diligent efforts to obtain the tax number. (This means you must make diligent efforts, such as calling or emailing the camp or sending a registered letter and giving them time to reply. You might even be successful in getting the EIN and then you can go back into the program, put in the proper EIN, and e-file normally.)
Assuming this was qualifying day camp, of course. If this was an overnight camp, it's just not qualified.
