Vostro 3560 is not charging battery

There is likely a fault with at least one of three items:

• the AC adapter
• the charging jack
• the charging circuit on the motherboard

It's a process of elimination to figure out where the problem lies, or at least where it doesn't lie. For example, if your AC adapter is recognized and works on another Dell laptop, then the problem is likely your charging jack or charging circuit.

Check if the light is lit at the plug end of the AC adapter or on the adapter block. And see if that light remains lit when you plug it into the laptop's jack. If the AC adapter's light goes dark when you plug it into the laptop, then the fault is likely with the jack or the circuit. 

Hold F2 while booting, to enter BIOS. See if the AC adapter is recognized.

Try another genuine Dell AC adapter of at least the same wattage/amperage. If that second Dell AC adapter works, then the fault is likely with your AC adapter. If it doesn't work, then the fault is likely with the jack or the circuit. The jack is a relatively inexpensive item that is not difficult to replace for someone experienced in working on laptops.

If a good AC adapter and a new jack won't work, then the fault is likely with the charging circuit on the motherboard, which would normally require replacement of the motherboard.

Also, it's worth trying a reset:

1. Disconnect all peripherals: printers; USB devices; media cards; USB hubs and extenders; etc.
2. Disconnect the AC adapter.
3. Disconnect the battery.
4. Press and hold the power button for 30 seconds to discharge any residual electricity.
5. Reconnect the AC adapter (without connecting the battery)
6. Reboot the laptop.

There is a centre pin in the adapter's plug (the end that connects to your laptop's jack/port). If that centre pin is broken or bent, then that is the cause. If it's bent, you could try gently to straighten it. If it's not bent, clean out the connector with Q-tip and 99% alcohol, and do the same to the jack.

Try slightly moving/jiggling the plug in the jack: if the light goes out or charging stops, then the problem is the charging jack or the pin in the plug.

Run Dell Diagnostics:
Press and hold F12 while booting to enter the One Time Boot Menu, select Diagnostics and press Enter. The Dell Diagnostics will test major hardware components. Choose to run extended tests.

If it turns out that the motherboard is the problem, it may not be worth buying a replacement. Given the age of the laptop, and that slightly newer laptops can be bought used for low price, it would probably be better to buy a newer computer to replace the Vostro.