What makes you think the hyphen was the reason? What was the exact rejection error code and message? Was it rejection code FW2G-502? If so, you have to be sure the Payer's name and EIN are being entered correctly; i.e., that the numbers are correct.
TurboTax always automatically inserts a hyphen after the first 2 numbers when entering an EIN, no matter if it's a W-2G as you described, or any other form such as 1099-G, 1099-MISC, 1099-R, or whatever. That shouldn't make a difference, even if your copy of the W-2G doesn't have the hyphen in the EIN. Did you otherwise enter the numbers (and Payer's name) correctly?
If an efiled Federal return is rejected, the efiled state return automatically rejects, too.
