In order for clarification, my GPU is Radeon R9 270x and my motherboard is Asus H110M-CS/BR, So after I installed the new fan for some reason the PC won't boot or give any sign of life, is there something that I can do to check or keep an eye?
First thing would be to check all your connections and make sure you didn't pull something loose. Have you tried to "jump" power with a tool on the mobo pins for the header (power) connector yet?
Likely something came loose in the process. Check that everything is seated properly..hardware and cables. You can also try a reset of the BIOS. If you disconnect the fan, does the system work normally?