NEC laptop won't power on

My NEC Laptop was idle for quite sometime, but I was able to use it the whole day yesterday with the battery in place and plugged in an AC Adapter and it was working fine, except the laptop and AC Adapter were terribly hot. Also, the Battery is not charging anymore and it says needs replacement. The following morning I cannot turn it on and has no sign of power on it. I appreciate your help with this.
 
Remove battery and try powering up on adapter alone. If it works, get new battery. If not, ...err..lets hold off on that for now.
 
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