Why is my pc plugged in but not charging?

I just received my Dell Latitude E5520 laptop refurbished on Ebay just yesterday. I have an issue where I’m trying to work on my computer but it isn’t charging despite being plugged in. I have tried troubleshooting, taking the battery out, and uninstalling the ACPI adapter. I used a different dell adapter but it says “No battery is detected”, so now I’m wondering if perhaps the issue is that the AC adapter is messed up and I need a new one. Could this be the case, or is the battery in need of replacement. Plus it shuts off after a couple minutes of playing the Sims.