The W-2C should not affect your Federal return at all since only the state income information has changed.
Based on the error information you shared, only the MN return will not be electronically filed. Take a look at your non-resident MN return when you have entered the W-2C and determine if it made a difference in the amount of refund you are getting from MN. Having the income zeroed out should allow you a refund of all of the withholdings since there is no MN income being reported.
If that is the case, you can consider filing your Federal return electronically and filing the MN return by mail. Be sure to attach the W-2C to the return that will be mailed.
@SBTX1
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