Fresh Windows Server 2003 R2 32-bit, just installed in a VM.
Oracle JDK 1.8 is not compatible with Windows Server 2003 R2 (it can be installed, but won't work correctly), so I've installed Oracle JDK 1.7 32-bit which is deprecated but should be okay to use it.
Downloaded Stash 3.9.1 Windows Installer 32-bit and tried to install it this way:
Step 1: Install a new Stash instance
Step 2: Destination Directory: C:\Atlassian\Apps\Stash\3.9.1
Step 3: Stash Home: C:\Atlassian\Data\Stash\3.9.1
Step 4: Startup menu (default settings)
Step 5: TCP Ports (default settings)
Step 6: Run as Service (selected). After clicking "Next" a message said:

It looks like a Stash service is already installed in the target environment.
The installation will replace any existing services. Do you want to continue?

Clicked "Yes"
Step 7: Clicked "Install"
The installer started extracting files, but after waiting for more than 30 minutes, it hadn't finished yet.
I tried to cancel the installation, but the installer never exited, so I had to kill the installer process using the Windows Task Manager.

Uninstalled Stash completely.

Tried to install Stash again, this time not installing the Windows service.
The installer completed in less than two minutes.
I didn't start Stash after the installer finished (last installer step).
Before starting the instance, I've verified STASH_HOME at C:\Atlassian\Apps\Stash\3.9.1\bin\setenv.bat
I manually executed C:\Atlassian\Apps\Stash\3.9.1\bin\start-stash.bat. The Command Prompt opened and closed immediately.
So, opened Command Prompt, navigated to C:\Atlassian\Apps\Stash\3.9.1\bin and executed start-stash.bat
I got this output:

To run Stash in the foreground, start the server with start-stash.bat /fg

Using STASH_HOME: C:\\Atlassian\\Data\\Stash\\3.9.1

Nothing else displayed.
Checked the Stash Home directory, and only a shared directory existed.

The instance won't start up.

All these steps have been done with the Windows default administrator, which should have full permissions. Even so, I've checked the user permissions in both installation directory (C:\Atlassian\Apps\Stash\3.9.1) and Stash Home (C:\Atlassian\Data\Stash\3.9.1), and ensured the folders allowed full permissions to the Administrator user.