IIRC you can actually install DX6 in NT4, it doesn't give you a full directX implementation it only upgrades certain parts of it but it will work. All other DX version ( well once i've got anyway ) version check and refuse to install but 6 will work, give it a try if you can find the Old DX6 installer about somewhere. If not i'll try and dig it out for you shoudl you really want to try it. It may not help the problem though.
The sound problems sound similar to ones i had in NT4 with my old PCI 128, no other problems but i could never get the startup and shutdown sounds to work, i gave up trying eventually.