My sister has the exact same problem but with Virgin Media Cable TV, I've pretty much taken the same steps as you with ABM, changed splitter's, cables, (no LNB for me though) i've even got a test line and changed provider with the exact same results. Some channels just wont work mainly HD ones. For example Sky Sports 1 HD is perfect, Sky Sports 2 HD just a black screen (but very rarely a pixelated image which would suggest signal issue), Sky Sport 2 SD perfect ?
Theres just no logic to the problem and no one seems to know what it is, highly annoying ! :-(