Hey there @livfe! I'll be happy to help!
So, this is a setting which I call Disabled SMC (I don't think that is the proper name). If you press and hold the power button and then connect either the power adapter or the battery, SMC will disable. So, the fan will spin extremely high, but the Mac will still boot. While the SMC is disabled, you cannot see battery information / power adapter information, nor can you close the lid to sleep (absolutely nothing will happen). I run Disabled SMC when I am diagnosing a power issue.
Now, that is what seems to be going on. I am sure you are not holding the power button while connecting the battery, so here's what to do...
***1) Disconnect the keyboard and try again*** (because the keyboard / keyboard connector on the logic board may be faulty).
***2) Check the Heat Sink*** (sometimes the thermal sensors can mess up and tell the logic board that the Mac is on fire).
***3) Try disabling SMC*** (holding the power button while connecting the battery or power adapter and then start up) ***and see if you get different results.***
***4) Try a different logic board*** (if all else fails, the logic board is probably shot).
I hope that gives you an idea where to go. Best of luck!