My Dell Inspiron Mini 270 power indicator won't turn off

Hello Everyone!
Ive been facing a peculiar problem with my Dell inspiron mini 270 of late. Its power light wont go off even after I switch off the laptop thus indicating that it is still being charged! What is even more strange is that in such a state I cannot restart my laptop until after the power light goes off on its own after a few hours. After repeated attempts, I have come to understand that this indicates that now the battery is discharged. Now when I put the power adaptor on and switch on the laptop, it starts. This effectively means that every time I charge the battery and switch off the laptop after some work, I HAVE to wait till the battery is completely discharged to start the laptop again. Guys, guys, I am at my wits end and have extremely close to tearing off my few remaining strands of hair. Any clues anyone?
 
If the battery is removable, remove and see if the light behaves... If it does, the battery may need to be replaced
 
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