a 7870 and i5 2500k will do 1080p 144 fps on CSGO effortlessly.
There are a few things to consider here
1) you must have a dual link DVI cable. Not simply a "DVI-D" cable, it MUST be a DUAL LINK DVI-D cable. No dvi-A, no dvi-i. Dual link dvi-D.
2) unless you are running integrated graphics, the motherboard has absolutely nothing to do with output frequency, as that is dictated by the monitor and graphics card. A 7870 is plenty for 144hz. I tested a gpu I gave away (r9 280x) and on csgo, 144fps was well within the threshold at max settings.
3) that said, make sure you're plugged into the GPU??
4) Your story about buying the 144hz and it not working doesn't make any sense. Refresh rate is determined by WINDOWS (your operating system), and it ALWAYS defaults to 60 until you change it, or it is even lower. I might be incorrect, but every high refresh monitor I've ever plugged in has always defaulted to 60hz until you change it.
Theres no reason the computer would restart either. At worst you would get an "out put out of range" error, and the screen would go black; not shut off.
I have a friend that has almost the exact same build as you, same motherboard, and runs a benq XL2420G with no issues.