There's no visible damage to other parts, I tried to turn it once after that and everything runs normally (fans etc run fine), but after a short period of time it just shuts itself.
Is there a chance that other parts are broken?
I am going to buy new parts on Friday so it's kind of urgent that I get a response since I'm going to use my old graphics card (AMD 6870 HAWK & Corsair VX550W PSU).
There are no other visual signs on the mobo itself. Everything starts out normal if you try to boot (tried twice on Wednesday and unplugged and wrapped GFX card and PSU in static bag) fans and everything run fine, GFX has all the red lights burning and CPU fan works fine, but it just shuts itself after like 20 s.
I would say you should be OK with the rest of your parts. My only concern would be what the real cause was. If it was just a bad mainboard you should be good to go but if the PSU was the cause of a overload you could kill the new mainboard to. From the reviews you have a good PSU but that does not mean it could not go bad. Just my thoughts.
you ps may still be under warranty to rma it. i would go to the vendor web page put in the serial number and see if it still under warranty. if it is i would put one in. with the video card it should be fine but other then putting it into another pc you cant tell if it fine or if it die in a week or in years. you need an o-scope and a load tester to see if your ps is fine under load.