To what was said before -
May have to delete any possible 1.15 files found, but there is a chance the uninstall exe and other similar files overlayed into the 1.16 folder. Installing patches is preferred to overwrite the previous patch entirely, for file issues do arise like this.
The most that could be done that I know is delete any files, until a more experienced member or staff member can help out. I did mention this to the rest of staff, to see if any of them know any ways to help out that are more effective.