I don't see how you made a mistake. Its pretty straight forward installing a card and should have booted right up. I don't want to run into this. Puzzled what could have been the problem. My system is Haswell based with a 4790K. I noticed you have the newest Skylake with the 6700. Was you running the latest mobo bios for that machine at the time of upgrade?
Also wondering now if the card will even work in my machine. Since it is 1 gen older then yours.
Its okay to make them thats how we learn. 
1st mistake - Thinking I can just install the new card update the driver and it will work. If you do this the new card will not work at all it will NOT run a monitor. You monitor will remain off plugged into a driveless 1080. Then I tried putting HDMI cable onto the integrated motherboard but it would not turn on as well. I then had to put in the old card back turn it on and figure out what to do. I tried installing the nvidia gtx 1080 driver, however the Nvidia software did not allow me to do this because I had the gtx 960 and it could detect it. So in windows settings I noticed the intel graphics was disabled. I realized I need to enable it in bios. Once I enabled the intel graphics it would not work because intel drivers were outdated. Once I updated the drivers intel graphics worked
I could turn the computer and use the gtx 960 or the intel graphics.
Now I was ready for step no 2. I swapped the cards again with the gtx 1080 now inside. However for some strange reason it messed up my scaling with the gtx 1080 (no driver) using intel graphics. Maybe this happens becuase it was an unknown card and both were enabled in system.
2nd mistake - messing up the scaling. I was lucky I could do this blindly and log in and get the settings window blindly to my monitor. This one sounds like a newbie mistake. Maybe there is a command or something through bios that would have fixed it ot some sort of widows command. Maybe if I disabled the GTX 1080 card slot then went to settings fxed the display and then enabled it, it probably would have been easier.
So yeah you need another graphics option to isntall gtx 1080 becuase Nvidia software will not allow you to install the new card driver with an older card. At least for me this was the case. Could be another newbie mistake.
Just putting this down in the event other experience this. I think I had some luck as well.
BTW you should check out the minimum system requirements if you are not sure if the card will work with your system. I was prepared for the worst and worst case scenario and I would have build a new system and passed it down to others. This is what I picked up as the minimum system requirements "3 - Recommendation is made based on PC configured with an Intel Core i7 3.2 GHz processor. Pre-built system may require less power depending on system configuration." Based on this I think you should be okay with your system.
Also, the HP computer out of the box we have is okay. However it can not handle VR and games like doom (ultra 1440p at 60 fps). There is a lot of positives with it, however I honestly wish I custom build my computer. I paid approximately $1300 cad in bestbuy when it was on sale. My new video card is over $1,000 plus the new psu I am like approx $1200. Therefore absolute game enjoyment you are better off building a system of your own. I still don't consider it a waste because I will pass it down to my kids when I decide to do a custom build. It is also good for total newbie that do not know much about hardware but like gaming. Definitely better then the comparable Dell option