Can you see the USB ports in Device Manager? If not, then you have a hardware failure. Now, there are several things it could be, one easy to fix, the others requiring a motherboard replacement, which is an expensive repair if the system is not under warranty.
The easy one is if the rear USB ports use a cable to connect to the motherboard. If so, that cable may have either failed or come loose. Replacing that cable, or simply plugging it firmly onto the motherboard USB header is fast and inexpensive to have done. Unless you are an expert, opening up a laptop yourself is not recommended.
If the USB ports are either directly attached to the motherboard (soldered in place) then either the solder joint has broken or the USB controller for the rear ports is shot. Fixing the solder joint is a job for an expert, and often fails anyway. If the controller is shot, or the broken solder joint cannot be repaired, you are looking at a replacement of the motherboard, and that will cost probably more than the system is worth.
My suggestion if you really need additional ports is to buy a USB hub for a few dollars and forget about the rear ports.