We have some NUnit tests that access the database. When one of them fails it can leave database in inconsistent state - which is not an issue, since we rebuild database for
I would do like phsr suggests for now and when you can afford it, refactor the tests so that they never have to rely on the same data that another test needs or even better abstract the data access layer and mock the results coming from that database. It sounds like your tests are rather expensive and you you should do all your query logic on the database and business logic in your assembly you don't really care what the results are that are returned.
You will also be able to test your ExceptionHandling a lot better.