Laptop fixed!

Older daughter appeared a week or two ago to tell me that her laptop died suddenly when she removed the power supply lead. After I explained to her that yes, laptop batteries do die pretty suddenly as a rule and that was the isue in her case, she stated that she was going to buy a new battery! "OK", says me, "but they are pretty expensive...". A few minutes later and I gather from the ranting that she finds £80+ for a new battery for a several year old laptop a bit much!

So life settled down to her using the thing plugged in to the mains charger. Then, one day, I am informed that the laptop has died. After further questions, it seems it randomly cuts out - simply shutting down instantly. I gave it a quick once over - waggling the power supply etc to check for loose connections - but nothing seemed obvious.
The machine was indeed simply stopping at random - somethimes Windows could be used for a few minutes, other times it was dying before the splash screen even loaded. Tried a live Linux disk - same issue, so not a Windows problem (but I didn't suspect that anyway as it was too sudden a shut off).
Ran Memtest+, but the machine died part way through. It didn't seem to be overheating (a common cause of this type of thing) and I had removed and cleaned out the fans about three or four months ago anyway.
So I went back to Computer Technician class theory and began removing non essentials to see if it made any difference. Having seen problems with laptops and batteries before, I took off the dead and useless battery.
The laptop didn't shut off! Despite running the machine for  hours, no shutdown! I gave it to my daughter who ran the machine all evening and then left it running overnight until she finished work the next afternoon - and it was still going strong!

So, when faced with a laptop which has no obvious issues with clogged fans or intakes etc, but it is still shutting down randomly, it is well worth removing the battery to see if there is some issue with that!
Several years ago, my wifes laptop had a dead battery and suddenly started having problems - but they were different - CPU running at 100% all the time etc - but caused by the dead battery.