There is likely a fault with at least one of three items: It's a process of elimination to figure out where the problem lies, or at least where it doesn't lie. For example, if your AC adapter is recognized and works on another Dell laptop, then the problem is likely your charging jack or charging circuit. Try another genuine Dell AC adapter of at least the same wattage/amperage. If that second Dell AC adapter works, then the fault is likely with your AC adapter. If it doesn't work, then the fault is likely with the jack or the circuit. The jack is a relatively inexpensive item that is not difficult to replace for someone experienced in working on laptops. If a good AC adapter and a new jack won't work, then the fault is likely with the charging circuit on the motherboard, which would normally require replacement of the motherboard. At this point, it's likely that the fault is with the jack, since you also say that the plug fits loosely in the jack. Also, it's worth trying a reset: There is a centre pin in the adapter's plug (the end that connects to your laptop's jack/port). If that centre pin is broken or bent, then that is the cause. If it's bent, you could try gently to straighten it. If it's not bent, clean out the connector with Q-tip and 99% alcohol, and do the same to the jack.
I have never charged this laptop before but it had a charge when I got it and worked great. Today the battery was low so I tried to charge it. The ring around the power plug on the power supply lit blue, but when I inserted it into the laptop it died. I tried it again, same thing. When I unplug it, it stays dead until I unplug from the wall outlet and plug back in, then it's blue again. And again if I plug it into the laptop it instantly dies. I unplugged it from the laptop and the wall, plugged back into the wall, and it came on, so I checked the voltage. Voltage from the outside of the barrel to the inside of the barrel is 19.66 v. But from the outside of the barrel to the center pin is 0. I removed the battery from the laptop and plugged it in. No difference, it instantly drops to 0 voltage. So it appears the power supply comes on, but gets turned off instantly when I plug it into the laptop, with or without the battery in the laptop. And the battery was working until it ran down today. Could this be the wrong power supply? The one I have is number LA130PM190. The plug fits but is just a tiny bit loose.
Power supply dies when plugged into laptop