What sort of cladding or house do you have?
We have a similar issue. It's a hardie sheet house, but not a typically leaky one like you expect to see i.e. there's no fake stucco/cementing etc on it. It's just a pure batten and hardie sheet place, built in 1989, one of those fake tudor ones.
The place was built with basically no eves, the spouting is nearly flush against the side of the house. We sometimes get issues in heavy windy rain around one particular part of the house, but it's so rare and brief that it will leak, but then not leak again for a long long time, so it never stays damp and everything inside is fine and without rot (I have done a lot of investigation around the area, when I first found it I removed some gib etc and had a good scout around, and it passed the building report when we bought it i.e. his moisture readings didn't bring up anything, and it's visibly dry). It has caused swelling of MDF scotia in that corner when it has happened though.
I'm a little bit at a loss about what to do at the moment and have been sitting on it. I have a builder friend who has said there's several ways we could permanently update the spouting/roofing system to make it so that the lack of eves is not an issue, but none of them sound cheap, even though I've not had official quotes.
Without looking at it, it sounds like the best solution would be to reclad one elevation (or the whole house), which is pretty expensive. Though if it's only leaking at the top, getting some decent flashings up in there should do it, which is still expensive (scaffolding is a killer).
If you don't mind the odd bit of water sneaking in (ie, leave it as is), just replace that scotia with some pine stuff. MDF is ruined as soon as it looks at some water.
Also, are you sure it's fibre-cement Hardies, not asbestos Hardies? 89 is towards the end of the asbestos cladding, but that makes a huge difference to cost.