I am trying to use AppStyleGlow.isl used in the sample Infragistics reference app. It turns out the dropdown button does not display with this style sheet, yet the control dropdown will drop if you click on the section of the input box where the button would be if it were visible.
So now the question is, what do I need to change in AppStyleGlow.isl for the dropdown buttons to display?
That sounds like a "bug" in the ISL, you should probably report it as such. You could search through the text of that file and look for the phrase "DropDownButton" (you might have to try just 'DropDown"). Assuming you find the DropDownButton role, the problem might be obvious like a transparent foreColor, in which case you can just change it and then you'll be able to see it.