Try the generic reset in the welcome sticky in this forum FIRST. Then get a repair estimate.
I removed the battery from my laptop and didn't insert it back properly. After I switched on the power the battery indicator doesn't show so I had to leave it to charge for a while without knowing that I didn't insert the battery properly. When I came back I found out that the laptop is very hot and stil no power indication.I tried put the battery properly and leave it to cool for a while, but couldn't restart the laptop as there's no power coming through. The laptop is 4 years old and is Asus X51RL.