Q: iPhone won't start up past Apple logo

I dropped my iPhone 5S and now it won't turn on fully.. I can charge it and the battery signal shows up to show its charging then shortly after it will go onto the Apple logo as if it were about to start up then it suddenly goes to a blue screen as if its on but the LCD is loose and can't get a picture but how can this be if I can see the battery and Apple sign?

I've took my iPhone the my local Apple shop to seek advice although the only way I can get it fixed is if I pay £200 (for screen repair and LCD repair).

Is there ANYTHING I can do to avoid paying £200? I don't have that money.

I haven't tried any other solutions to try fix it either, please help