New Zealand Law
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The problem you face is that you did inspect. That was of course a prudent step, but undertaken possibly in dry conditions. If you asked specific questions about the presence of water or any potential water problem, then the answers you were given would be important. The issue will be whether this does affect the use and healthiness of the house, or is a minor problem. You may need to look at the council records as well to see if the LIM report mentions a water or drainage issue.
The other issues like the keys, would normally be sorted on settlement, but again this does depend on what you were told by the seller, or the land agent. What they say before you signed the contract, to persuade you to buy, is critical. If they were silent, then there are no representations. If the promised things but did not perform, then you may have a claim.