Control phone with broken screen from computer? I'll just clear up the basics before proceeding as previous comments have just been talking about things that really haven't helped me get any closer to fixing this.

Have I checked out the broken screen tag wiki? 
Yes, filled with circumstantial answers that didn't really make any sense to me, every answer required something I couldn't do.

Use a USB-OTG cable?
Unfortunately the screen is untouchable. I can't see what I'm doing so I wouldn't be able to direct a mouse even if I could get one connected.

Basically, I have a Samsung Galaxy with a broken screen, touch screen also broke and USB debugging is disabled, can I still save this?

I just wanna be able to control it for a little before taking it to a store. I need to do some things, is this possible? Every answer I read just talks about circumstancials.

I actually might have USB debugging enabled, although my device isn't showing up when typing adb devices and simply prints List of devices attached with 2 blank lines after it.
This happened to me about 2 weeks ago. I search the web and couldn't find anything useful. What I did might seem ridiculous but it did the trick and I managed to not only get my pictures but also exported my contacts and saved them. This is what I did:

I connected an OTG cable to my keyboard and pressed the power on button to 'turn on' the screen. I typed the PIN code and pressed enter. Then very quickly disconnected the keyboard and connected the device to my pc (it helps having 2 cables, one with OTG adapter attached and one just with USB). This way I can see the files of the mobile and I can save my photos etc.

Now my problem was that my contacts were stored in the phone and I couldn't synchronize them because they weren't stored in Google. In order for me to export them I did the following:

Right after connecting with the keyboard and typing the PIN code, I took a screenshot (for Galaxy phones you can do that by pressing home and power buttons simultaneously). Then quickly again I would connect it in my PC and go to the screenshots folder and this way I could figure out where I was. It is quite hard at first but this way you can navigate anywhere you like just by pressing the arrow buttons and enter key. If at any moment you don't know where you are, you can take a screenshot. The disadvantage is that until you get to see the screenshot from your PC, the screen locks again and you will have to connect to the keyboard again and repeat the process but this way I exported my contacts, found them through my pc and imported them into my new phone. 

Hope that this helps...