If your W2 has an empty Box 1 and has a figure in Box 12 Code J (third party sick pay), then it is not required for you to include this W2 with your tax return.
Third party sick pay (Code J) is not taxable. Your employer is required to create the W2, but it is not necessary for you to file it.
Also, if you try to submit a W2 with a $0.00 in Box 1, the IRS will reject your e-file.