Chevy doesn't shift through gears

Hi, I have problem with my clutch/transmission, it doesn't want to shift on any gear while clutch being pushed to the floor, the only way to change gear is turn off the engine, put on first, and turn it on again. However, the car starts to move even with full clutch on the floor! After that, its hard but possible to change gears, the sequence is that: (engine turned off)->first->start the engine->third(its impossible to change to the second gear from first, also if you on second gear and push the brake, you can shift from second to neutral!)->(If there is a red light then second or neutral)-> else gear 4 and 5.