If it doesn't even start when connected to the power adapter (that's not really clear from your story), reset it by removing the adapter and the battery and keeping the on-off switch pressed for one minute. Then insert the battery again, connect it to the power adapter and see what happens.
If that doesn't help, things to try are (1) a new battery, (2) a new motherboard and (3) a new laptop.
two days ago I worked with this laptop while it plugged into the switch. Usually, it has this blue color bulb on as a battery charge indicator. But when I removed it for the power it still lights up in blue. I shut down the laptop and day after that indicator is still on. But the laptop won't turn on. Can someone tell me why is this happening and how to fix it?

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