How to flash a rom on an entirely blacked out phone (s5 mini G800H)

Three or four months ago, whenever I tried to connect to Play Store or my gmail account etc. my phone returned a network related error message, which happened after I made a factory reset. Some games encountered errors too. I tried to flash a rom from sd card, but it did not install even though it said that installation was successful. Odin doesn't recognize my phone, and there is no root, so rom installer won't work because I can't install custom recovery without root (correct me if I'm wrong). In this desperate situation of mine is there at least something I can do (except buying a new phone)?