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Is the AC adapter hot or in a hot location? If so that may be interfering with the charging cycle.
Check Battery Info and Battery Health in the BIOS (F2 at startup). Call Dell if there's something of interest to report.
Have you tried shutting down the computer, disconnecting the AC, and removing the battery? Upon reconnecting maybe it'll resume charging.
The battery may be defective. See if you can test it in another laptop.
If the battery is OK, the inability to recharge is either a bad power supply/plug or a problem with the socket on the laptop. A socket connection can break loose from the system board from pressure on the power plug. The power plug has a third wire that tells the computer what charger is being used. If the plug is bad, the power supply can be replaced. If it is a connection on the system board it might be fixed by disassembly and careful soldering or replacement of the socket. The extreme solution is replacing the system board, ~$500. If the adaptor will power the computer, then the problem is either the third wire in the plug (you can see it inside), or the third wire connection of the socket to the system board.
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