n33m

Hey guys,
Yesterday I seem to have burned through my Nvidia 870M GPU, which is built into my C504 Schenker Notebook.
Since it is integrated onto the motherboard, as far as I know, it's not replaceable and I will have to buy a new setup.
This time I want to get a desktop PC since the portability is not worth the price, atleast for me.
I don't know too much about which motherboard works with which GPU and CPU so I'm seeking your guys' help.
1. Budget & Location
 
 I'm from Germany, as you might have noticed by my English.
I plan to use a budget of something between 1000-1200€.
I would want to rescue a Samsung Evo 850 (250GB) from my old rig, so I wont be needing that in the new build.
 
2. Aim
I will be using this build mainly for gaming. The games I play are mainly stuff like CS:GO, LoL, PUBG and DotA 2 (I guess as mainstream as it gets)
I don't put too much emphasis on the way things look but of course I cannot get enough FPS.
Therefore, I aim to have a Nvidia 1070 or another similar GPU in my rig (if that fits into the budget).
I also was interested in the Intel i5-8400 but I'm not sure either if I can afford it with my budget.
I don't care at all about any RGB stuff or how the case of the PC looks. Functionality > Looks.
 
3. Monitors
The monitor I use is a newly bought Asus VG248qE (24", 144Hz) and I'm not necessarily looking forward to buying a extra monitor.
 
4. Peripherals
I don't need any other peripherals since I'm happy with my Logitech G19 (yes that still works), my HyperX Cloud II and my Roccat Savu.
 
5. Why are you upgrading?
I'm almost certain that my GPU is broken and due to the notebook I'm using, its not possible to change the GPU.
The rest of the laptop works fine, so I would try to sell it for 200-300€, which I might be adding to my budget.
 
 
I hope someone can help me with my situation and I'm looking forward to my new setup.
 
Thanks in advance to anyone helping!
Merry Christmas in advance