You don't open an .exe file. An .exe is usually a program. You activate a program. If the program is written to start up something, or starts with a setup, or whatever, it really all depends upon what the .exe is supposed to do.
Since it sounds like your .exe starts up a setup ... and then nothing happens, it sounds like your downloading is somehow corrupting the .exe.
Go to some other website, that you know has worked in the past; get some .exe file that you know has worked in the past and try again.
You could even try downloading an .exe that you already have, and then compare one to the other (you can use the DOS FC /B file1.exe file2.exe command). The files should be the same.
I recently have been having trouble opening up .exe files. After downloading a .exe file when I click on it it goes to the setup and after I click on that nothing happens. This problem has been getting very annoying over the past few days and I would highly appreciate it if someone could help me.