laptop - Sony Vaio VPCF115FM screen broken and external display output not working under Win7 x64

I have a Sony VAIO laptop series # VPCF115FM model # PCG-81114L in which the laptop screen is broken (smashed that is, cracked I say), no picture at all, not all black, mostly white, that flickers and changes a bit as the computer boots up (It appears as if a video signal is being sent to the laptop display). I bought this on the cheap - 50 bucks - fixing is not economically viable/ practical at current market rates, ~200$ @ 2015 dollars. It works, I know it works, I've installed Linux on it. No problems at all, just pop the Ubuntu installation into the drive and it displays right nice through the VGA display port onto an external monitor.

Now my question is how in the hell do I install Win 7 on this machine? Ultimately I want to update the BOIS in order to fix 'the know issue of over heating and thus the crazy loud fan noise' and (and maybe or) I want to install Win 7. Seems simple enough, right. Wrong!

While trying to install Win7 on the laptop it does not display on the laptop screen (of course! its broken!) or through the external display output. That's the problem! The laptop has VGA and HDMI outputs. I've mostly tired just the VGA output. I've tried both 'Win 7 Installation Media' and WinPE to boot/install to no avail both with and without the laptop screen-lid open or closed shut and with an external USB mouse/keyboard, neither display through the VGA output port on to a external monitor, at all what so ever.

My thinking, was I could use a 'technical computer' (a computer with different hardware that is used to setup/configure a Win 7 installation in order to deploy on computer with different hardware) to install Win7 onto and then use Microsoft 'SYSPREP' tool to do a 'system audit' and generalize the computers hardware and then transfer/swap that hard-drive to the Sony Viao laptop. I tried this, and it sort of seemed to work. Video didn't display, but I heard the windows chime start-up sound. This gave me hope that the installation I made was working, kinda working. I tried fn+f7, 'windows key' + 'P' and a few other keys, didn't work. Maybe it wasn't in the right order? The Win 7 installation that I made using this method works, I am using it right know as I type this (on the technical computer) after I transferred it to the Sony Viao Laptop and then back onto the technical computer after I repaired/fixed the installation by using a image I made of the installation that I created earlier.

The laptop does not display the boot up screen during boot up.

So far I've only gotten Linux Ubuntu to install and display onto a external VGA compatible monitor. Normally I close the laptop lid right after I turn it on, with a the USB keyboard/mouse pluged in. I believe that the Sony laptop has a Nvidia graphic card (there's a sticker on the case), I don't know what kind though.