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Alright, I failed to read the error in its entirety. Error 28 means that MySQL is not setup properly. Basically, it means that MySQL does not have enough "working space" so it can't do what PunBB is requesting. You need to contact your webhost and tell them to fix the configuration so that MySQL has more room. There really should be no less thana gigabyte of room for MySQL on a standard server.

The reason it needs this extra room is because for most of what MySQL does it creates temporary tables for itself and that requires quite a bit of space depending on the size of your database. Count yourself lucky though. I've lost an entire database to error 28 before. Had to go to a backup that was 12 hours old all because the webhost negligently didn't give MySQL enough space for its tmp directory.

For more information on MySQL error 28, go here. It'll say exactly what I have said with quite a bit more technical jargon.