I see two issues with the code you have posted:
The first being there are two semi-colon's missing after 2 of your 3 cout's (the first and the third, as underlined below):
using namespace std;
cout<< "Main Working"
bool Running = true;
cout << "Loop Working";
sf::Window App(sf::VideoMode(800, 600, 32),"Hello");
cout << "Screen Working"
This causes your program to think that a certain line ends in a place different to where you want it to, which can lead to undesired effects (although, why your compiler isn't throwing up some sort of error puzzles me).
Secondly: sf::Window should only need to be created once, outside the (while) loop. When I tried the same as your code, in my IDE, I had a window being created and destroyed over and over, whilst the loop ran. This lead to an effect by which a window would open and close every couple of seconds (maybe this is something your compiler doesn't like and crashes the program for you, I'm not sure, please correct me if I am wrong).
Try it with these and get back to us, if anything, it might not fix the problem, but allow a new (debugger tracked one) to be picked up.