Speakers don't turn back on after removing the heaphones

The way you described convinced me that your audio driver is OK, but the sound can be heard through the headphone only. If this is the case then you have a mechanical failure (metal fatigue) on the head phone jack assembly.
I consists of two DPDT switches ganged together in a small housing with have 3mm jack on it. The leaf spring contacts failed to make after the headphone plug is detached. Only skilled technician can remove it from the PCB then sold an new one in.