I do not compile your file. It's big and may contain more than one error with Cut operation :)
So, I wrote a working sample for you. Try this:
////////////////
// vars
Standard_Real cylRadius = 15.;
Standard_Real cylH = 150.;
Standard_Real boxL = 100.;
Standard_Real boxW = 80.;
Standard_Real boxH = 50.;
TopoDS_Shape resultBox;
// make Box
BRepPrimAPI_MakeBox myBox( gp_Pnt( 0, 0, 0 ), boxL, boxW, boxH );
// make axis of direction for cylinder
gp_Ax2 cylAx2(gp_Pnt( 50, 50, 0 ), gp_Dir( gp_Vec( gp_Pnt(0,0,0), gp_Pnt(0,0,100) ) ) );
// make cylinder
BRepPrimAPI_MakeCylinder myCyl( cylAx2, cylRadius, cylH );
// make Cut operation and get result
resultBox = BRepAlgoAPI_Cut( myBox, myCyl.Shape() );
// show myBox
Handle(AIS_Shape) myBoxAIS = new AIS_Shape( myBox );
myAISContext->SetColor( myBoxAIS, Quantity_NOC_RED );
myAISContext->SetMaterial( myBoxAIS, Graphic3d_NOM_SHINY_PLASTIC );
myAISContext->SetDisplayMode( myBoxAIS, AIS_Shaded );
myAISContext->SetCurrentObject( myBoxAIS, Standard_True);
myAISContext->Display( myBoxAIS );
// wait
Sleep(1500);
// show myCyl
Handle(AIS_Shape) myCylAIS = new AIS_Shape( myCyl );
myAISContext->SetColor( myCylAIS, Quantity_NOC_GREEN );
myAISContext->SetMaterial( myCylAIS, Graphic3d_NOM_SHINY_PLASTIC );
myAISContext->SetDisplayMode( myCylAIS, AIS_Shaded );
myAISContext->SetCurrentObject( myCylAIS, Standard_True);
myAISContext->Display( myCylAIS );
// wait
Sleep(1500);
// delete objects
myAISContext->Erase( myBoxAIS );
myAISContext->Erase( myCylAIS );
// show result of Cut
Handle(AIS_Shape) resultBoxAIS = new AIS_Shape( resultBox );
myAISContext->SetColor( resultBoxAIS, Quantity_NOC_MATRABLUE );
myAISContext->SetMaterial( resultBoxAIS, Graphic3d_NOM_SHINY_PLASTIC );
myAISContext->SetDisplayMode( resultBoxAIS, AIS_Shaded );
myAISContext->SetCurrentObject( resultBoxAIS, Standard_True);
myAISContext->Display( resultBoxAIS );
// THE END
////////////////