yes, noticed the mistake after submitting.

and why conditions?

The kata specification assures us that the parameters are in range, so there's no point in checking.
Further, checking you are doing is insufficent and misleading. You check for too low, but not too high. And it's wrong. Given Past(-1, 1,0) will return 60000, but it's an invalid time. There is no correct answer. If you needed to check the range, it should be:

if (h <0 || h > 23)
    throw new ArgumentOutOfRangeException("h", "Hour must be in range (0...23)");

A good idea...