What happens if you remove the battery and run on AC adapter only?

Please list Dell model number and version of windows. Example: Dell Inspiron 3543, windows 10

If you don't know, enter the service tag number onto the link below. After, you should see your Dell model number in the Dell Product Support page.

Support | Dell US

https://www.dell.com/support/home/us/en/04

Please view video in link below if you don't know the service tag number

How to find a Dell Service Tag (Official Dell Tech Support)

https://youtu.be/sDPVSHHN-SY

 " Dell inspiring 5558 and windows 10 "

" The LED on the adapter is turning off immediately after connecting it to laptop" usually indicate an issue with the computer's motherboard. Now, if you haven't remove the battery yet, I like you to remove it to see if that will make any difference. Please follow steps below. 

1. Power off system. Remove AC adapter and all peripherals.

2. Close the display and turn the computer over. Slide the battery latch to the unlocked position. Remove battery

3. Press " Power On" button for about 20 seconds then release. Replace battery, AC adapter, power on, hopefully  computer starts normally and LED on adapter doesn't turn off.

Removing battery - Page 13

https://topics-cdn.dell.com/pdf/inspiron-15-5558-laptop_service-manual_en-us.pdf

Note: Please use a can of compressed air to blow into the DC Jack and around the ID pin. This will blow out any debris or dust that might have accumulated.

If the troubleshooting steps doesn't fix the computer, I'd suggest using your computer warranty by contacting Dell Technical Support in the link below:

Contact Information | Dell

https://www.dell.com/support/contents/us/en/04/category/Contact-Information

If the computer is out of warranty:

How to arrange an 'Out of Warranty' repair on your Dell System

https://www.dell.com/support/article/us/en/04/sln284409/how-to-arrange-an-out-of-warranty-repair-on-your-dell-system?lang=en