Laptop stopped acknowledging charger, now it has died and can't be turned back on?!

Once again, I come to the reliable nerds here, a supplicant, seeking your wisdom. I have a Dell Elitebook running Windows 7 Professional, refurbished, haven't had it that long.

The other day I had it plugged in and was listening to music like usual while doing some other stuff around the apartment. After a few hours of no trouble, I noticed that the "charging" icon wasn't lit up anymore - the laptop had stopped acknowledging the charger at some point. I couldn't find any kinks or anything in the power chord. Finally, I tried two other chords, but to no avail. No acknowledgement. So then the battery died not long after, and now I can't turn it on!

What could have happened? Can it be fixed? And if not, can some files I had on it that I hadn't gotten around to backing up on my external hard drive be recovered from it? I have very little tech knowledge at all, and I certainly don't have any complicated equipment. I don't mind if I have to get a new computer, it's just that I've been having a lot of trouble finding ones that don't run Windows 10 these days, and also I really want the music files off this one. Can anyone help?

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