Hi @eaglei
Check that there is power available at the motherboard at the plug end of the [https://www.ebay.com/itm/254920759310|DC-In jack] (aka power port cable)
The cable connection is shown on p.34 of the [https://downloads.dell.com/manuals/all-products/esuprt_laptop/esuprt_inspiron_laptop/inspiron-15-3537_owner%27s%20manual_en-us.pdf|owner manual] in the section dealing with the removal of the motherboard.
With the charger connected, if there is no voltage at the end of the cable then the DC-In jack will have to be replaced as it cannot be repaired. Search online for ''Dell 3537 DC-In jack'', to find suppliers that suit you best.
If there is 19V DC between the red and black wires of the cable at the plug, then here's the [https://www.alisaler.com/dell-inspiron-15-3537-compal-la-9981p-rev0-2-schematics/|schematics] for the motherboard, as these will be needed to find out where the problem is on the board.