Two possiblities:
1. The power supply is not working, or the cable from the brick to the power jack is damaged. The easiest way to test this is to test it with a known good power supply. If yours is defective, a reasonably priced replacement may be available.
2. The power jack in the machine has broken solder joints or is otherwise not making contact with the plug from the power supply. If this is the case, a skilled repair technician should be able to tell you if it can be repaired and, if so, what it will cost. The worst case (most expensive) situation would be that the motherboard is damaged and would have to be replaced.
Sadly, we live in an era where it can cost more to repair a machine with a relatively minor problem than to buy a new one.
Good luck. 🙂