1) Check if your battery is still good.
If it was left totaly drained for some time, it's dead and need to be replaced. Some time bay be as short as 2 or 3 days. A Li-ion battery MUST ALWAYS have at least some charge in it.
When totaly charged, it should be removed from the charger. Leaving a Li-ion battery in charge mode for longer than needed will damage it. The laptop can run from the charger only without the battery been present.
2) Check that your charger is correctly plugged into some power outlet. Make sure that that outlet is effectively woking. Plug a desk lamp, or anything else that you know is in working condition, in the power outlet to see if it works.
3) Check that the cable from your charger is intact.
For points 2 and 3, if you find a fault, replace the charger.
Maybe the power switch is defective. ou need to open the case to replace it. It's probably welded in place. Relatively easy to replace with the correct tools.
Maybe there is a fault on the motherboard itself. In that last, and worst, case, you need to replace the whole motherboard. It's probably much cheaper to replace the whole computer.