Gateway nv59: "We couldn't update the system partition" Can't install

Update: Everything is clear now!
1. Deleted every partition that would allow me .
two partitions remained, the main C 289GB drive and one 9GB drive that Is unallocated. I can't do a thing with it, format it or rename or merge.

2. I then hooked up an hdmi cable to my tv, this seemed cause a "flicker" on the screen. Then I rebooted the system
3. Installed the OS again
4. When it rebooted I removed the FLASh drive. On other computers, this isn't necessary but for mine it gets stuck if its still in there

I have owned and built several computers and recently just installed WIN 10 on a friend's laptop from scratch. The gateway I have has been the most headache of all time with every problem under the sun, most of which didn't have google search results and I had to come up with my own conclusions

Thanks to your assistance I was able to get the right path!

Glad you got it working finally - that is really weird about those partitions not being able to be changed, though.