Is the adapter frayed? When you plug in the adapter to the system, does the adapter jack hold still and firm or does it fall off easily? The alternate adapters and batteries you have tried, are they Dell products certified for your system model?
Restart the system and press f2 key to enter BIOS - check the adapter status with and without the adapter connected. Also, wiggle the adapter jack while connected to the system and check if the adapter status changes at any point in BIOS.
Restart the system and press f12 key on startup - choose diagnostics. Let it run the diags and if you encounter any errors - make a note of the complete error and report the same to us.
If the system is under warranty, write me a private conversation with the service tag and your contact details. If there is no warranty, then we can help with a paid service call if required.