My 7520 will charge until the battery reaches 100 % after that it won't keep it charged and the battery drains until it is dead, even with the charger plugged in. After a while (a day or two) I can plug the charger back in and it will start charging, but only after it died. If I plug in the charger in at say 50% it will not begin to charge.
Are you using an original Dell OEM Adapter? When you plug in the adapter to the system, does the adapter stay firm or does it fall off easily? Is the adapter frayed? Is there any damage on the system? Could you test with another power adapter if possible?
Restart the system and press f2 key to enter BIOS - check the adapter status in BIOS with and without the adapter plugged in. Also, wiggle the adapter cable at the end and see if the status changes in BIOS at any point.