Restoring QT wallet on Web or Mobile using private key?

Quick odd question that the best Googling could not find the answer for:

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I have an old QT wallet on a junky laptop that has a broken network adapter. I have the .dat file, but I ALSO have the private key that I exported from the console way back when…

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Is it possible to restore the QT wallet on either a web wallet or the mobile wallet using only the private key?