The 2004 North Carolina exit poll said that John Kerry got just 27% of the white vote. But as we've written before that survey also supposed African Americans were 26% of the electorate in the state when they were actually 19%. That means Kerry actually did much better with white voters than the exit poll indicated.
The non-white vote was about 21%. Assuming Kerry got about 85% of that, it accounts for 18% out of the total 44% he received in the state.
That means he derived his other 26% from the 79% of white voters in the state. That would put his share of the white vote somewhere in the 32-33% range.