Hi all! Long time reader, first time poster. 
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A user came into our office some while ago complaining that they were unable to use their laptop without the power cable plugged in. Every time they tried, the machine would simply turn off. They had struggled along for a week or so but were finding it increasingly annoying so they came to see us.
The laptop in question was an old reconditioned unit that we managed to salvage from that year’s refresh and had re-purposed for the new user. They came into the office and placed the offending article on the desk.
Sure enough, when we pushed the power button without plugging in the cord; nothing happened. We plugged it in and fired it up and all seemed fine. Once Windows was running I checked the power icon and there were no signs the laptop was charging, or that there was even a battery there. We’d had this laptop for many years and had not experienced a single battery failure. I figured that this was a one off issue and turned off the laptop.
Turning the laptop over, however, revealed the true cause of the issue.
No battery.
At some point it had dislodged itself and was later found sitting in the bottom of the laptop bag. Sure enough, once the battery was re-seated, the laptop became far less picky about being removed from the external power.
The user left feeling rather sheepish but good-natured about it all the same.
Happy Ending!
[Picture Source: jadijadi (CC)]