OK, I am starting to put it together little by little. I was mistaken about your C: drive. Your actual SQL Server is on the C: drive. I wouldn't worry about that. That is just what your user databases are connected to. There are permissions there, too, but you won't need to worry about them.
You .xml file is fine. It just shows that your database is located in the 32-bit Program Files. I am a little confused, because generally, be default, Program Files x86 and Program files for the 64-bit programs would be located on the C: drive. And, by default, applications get installed into one or the other.
It appears like when the default path to install the program came up, it appeared like C:\Program Files x86\Amazing Charts, and you changed the C to a D, which would be fine and would put your databases on your data drive.
If you right-click on the same .xml file from above and check its permissions, does it have your staff user groups on it?
One thing when troubleshooting it to make things as simple as possible. I cannot see what is happening, but it sounds as though users are considered domain users by virtue of being in the staff group. You could just log in directly as a user and make sure that user has permissions.
Or maybe put the group "Everyone" in the share and in the NTFS permissions and make a test user with user permissions. Log into a computer with the test user. It should be able to log into Amazing Charts.