Sounds like your Dell didn't close properly when last shut down/shut off. The clue is the indicator light on before you plug in the adapter, suggesting the notebook is still on, perhaps in sleep mode, instead of shutting down normally.
You might try the following:
1) unplug the adapter & any other external devices from your Dell
2) remove the battery from your Dell & set it aside
3) press the power on button 10 times at 1 second intervals (an analog watch is handy, with a second hand, to time the intervals 1 second apart) This is done to discharge voltage in the circuits & help the memory chips forget whatever they might be retaining.
4) press & hold the power on button for 30 seconds (one continuous interval) This has the same purpose as #3
5) replace the battery; plug in the adapter; press power on as you normally did before this problem came up
6) It might boot normally into the OS. If it does, leave the adapter plugged in 'til the battery is fully charged as indicated by the power icon in the tray. You may have to click that battery/power icon in the tray to get the reading on the battery charge. If you don't want to wait for the battery to charge fully & check the reading, just leave it plugged in overnight, & check the battery charge reading in the morning. You can use the Dell normally while the battery is charging.
7) If this doesn't work, you might open the door covering the memory chips or open the case for access to the memory chips, & check to see that the memory chips are seated properly. You might also try replacing the memory chips with known, good memory chips if reseating the originals doesn't help. Bonne chance!