Connect Windows 7 Laptop to Mac mini
I have a similar scenario in that I need to access a Linux system on my LAN from my MacBook Pro, so I use the free version of NoMachine. It's available for Windows, Linux and OS X.

You first have to hook up a monitor, keyboard, and mouse to get NoMachine installed and configured on the Mac and then connect at least once from the Windows system.  You could then shutdown the Mac mini, unplug monitor, keyboard, and mouse and then restart the Mac mini.  I'm assuming you also have it set to auto login.

It would need to be installed on both the Windows and Mac systems.