I believe Win 7 removed support for DOS executables, so DOSBox is the only way to go. Remember that the path in DOSBox is not the same as the path on your computer. Assuming the TyrHack directory is being mounted as drive C: and that directory contains tyrian.hdt, the directory you would set in the .ini would be C:\
It can be a little tricky in dosbox as you have to remember its usually setup to see C:\ as actually C:\games mostly so you keep dosbox in its own games directory. Made more confusing for me as my real games drive is actually g: and dosbox sees it as c: when its setup I spent ages messing around until I remembered that fact haha.
I have tyrhack in G:\games\tyrian\data\ which is also where the tyrian.hdt is but dosbox sees it as c:\tyrian\data so that is what you need to change the tyrhack.ini directory to for it to work.