Not shifting, but starts and no codes?

My car starts up, but the gear shift is loose and will not change gears. It drove all day, but in the later evening, it went loose on me. Normally there is a bit of feedback when shifting gears, but now there is not. We were thinking the shifter cable or the solenoid, but we are not sure. Is there a solenoid under the center console with the shifter cable? How do I go about repairing this without taking the vehicle to a shop?

My brake lights work when the car is turned on. But nothing happens when we try to put the vehicle in reverse.