switching between 2D and 3D with Picking - c++

Question

So I'm trying to make a menu , and when I select an option I want it to draw the scene and to be able to pick from the scene in order to run the game. The game is checkers. I can do this without the 2D Menu, I perform the picking and the game is fine. But when I add the menu and try to switch between both, either I get no image (all black) or I set a perspective view and the Picking is no longer available in the same range.
to setup the 2D I make:
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(0, 600, 600, 0, -1, 1);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glPushMatrix();
//draw 2D
to setup the 3D I use
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
gluPerspective(45.0, (GLdouble)600/(GLdouble)600, 1.0, 200.0);
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
//draw 3D
With this I'm no longer able to pick objects from the scene, but I can pass from 2D to 3D and watch the entire scene.
To perform the picking:
void PickInterface::performPicking(int x, int y) {
glSelectBuffer (BUFSIZE, selectBuf);
glRenderMode(GL_SELECT);
glInitNames();
glMatrixMode(GL_PROJECTION);
glPushMatrix ();
GLfloat projmat[16];
glGetFloatv(GL_PROJECTION_MATRIX,projmat);
glLoadIdentity();
GLint viewport[4];
glGetIntegerv(GL_VIEWPORT, viewport);
gluPickMatrix ((GLdouble) x, (GLdouble) (CGFapplication::height - y), 5.0, 5.0, viewport);
glMultMatrixf(projmat);
((PickScene*)scene)->selectMode=true;
scene->display();
((PickScene*)scene)->selectMode=false;
glMatrixMode (GL_PROJECTION);
glPopMatrix ();
glFlush();
GLint hits;
hits = glRenderMode(GL_RENDER);
processHits(hits, selectBuf);
}