One zero-cost thing to try:
1. with the laptop computer powered-off, remove the battery
2. disconnect the power-cord
3. hold-down the on/off button for a few seconds, to drain any "residual" electrical power from the motherboard
4. reconnect the power-cord
5. does any lamp light up to show that the laptop acknowledges that it is receiving AC power?
6. if so, try a power-on
7. if not so, then the battery probably has 0% remaining power -- it previously ran down to that level
8. consider either a dead power adapter, or a broken jack where the power-cord connects, or a dead motherboard.
Good luck!