Back up anything important and try a factory reset.
If you have the option in recovery mode, try wiping the system cache (just the cache, not cache+data, not factory reset). That was removed from most phones a while ago, but I'm hoping that a phone I've never heard of might still have a useful legacy feature like that. There's a small chance that that might fix it, in which case you are spared a reset. But otherwise my best guess is that you've got some corrupt data somewhere that's messing up the display drivers, and I doubt I'd be able to track down precisely what (and if it's system data I might not be able to remove it anyway without root), in which case a reset will be needed.
The worst case is that the actual system software has been corrupted, in which case a reset won't help either (in that case either a reflash would be needed or, if the storage itself is damaged, there would be nothing you could do). But I think there's a good chance of a reset fixing it. From what you describe it's clearly a problem with the android system rather than the hardware, since the splash screen and boot animation work (which all come up before the Android system takes over).
