Many thanks for your replies. I cleaned the fan and other vents with compressed air. There was dust but not that much I expected, considering the fact that the comp. stayed in a dusty place for more than two years and it got its first cleaning in 3 years.
I'm also ordering a new power adapter. I came across an old post in some other forum that in Lenovo 3000 computer keeping a dead battery while drawing power from mains is not the best thing to do as that might lead to some 'stability issues'. I was just doing that
Now I've removed the dead battery and for the last one hour or so the machine is running normally. Touch wood.
So far I remember that the light just goes off without any flickering while blackout.