If I have put a verification code from one of my W-2's in TurboTax information 3 times and it does not accept it, what do I do? Should I file by mail?

Try to leave it empty. The IRS states:

Taxpayers and tax professionals are urged to enter the verification code when prompted by software, as it can speed the processing of the return and the issuance of the refund. However, omitted and incorrect verification codes will not delay the processing of a tax return.

Let me know if this works.