So I ran into the old plugged in, not charging problem with my laptop about a month back. I hoped it was the charger, but upon getting a replacement 65-watt charger, the problem persisted. I assumed the fiddly bits on the inside of the laptop had given up the ghost, as I've had that issue before, but when a friend plugged in his 90-watt dell charger it worked like a charm. I'd rather not have to go buy a new 90-watt charger, but I will if I have to.
Also, I suppose I should mention that I'm using a 5759 with no modifications. Also, I used to get an error message every time I plugged in a 65-watt charger though it doesn't show up anymore for whatever reason and I can't remember exactly what it said. Something about it not being recognized or somesuch. Same error message with 3 different 65-watt chargers.
The 90W charger that you had tried, which system model was that specific for?
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. Check the battery health in BIOS (if applicable).
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.These are onboard diagnostics and they might possible pick some error if the hardware is not functional.
Since you have tried different adapters, I would suspect the next component to be replaced is the DC port - you would need this part - http://bit.ly/2cLaDWJ
Also, please click my DELL-username and write me a private conversation with the service tag and your contact details(Name and Email) for case records.
Let us know if you have any other queries.