I'm really surprised. I own 3 Paperwhites including a 1st edition and all are still working great. I do keep them in excellent cases (Fintie Folio).
If it still seems to charge, try a reset: hold the power button on for 30 seconds or until you see it start to reboot. See if that will revive it. This procedure does not delete any data or settings.
Also check if you Paperwhite is still under warranty. The base warranty is 1 year so find your purchase date. If still under warranty, contact Amazon immediately and they might exchange it for a refurbished unit.
If your Paperwhite is NOT still under warranty then you could check if you damaged the charging port. Such damage is caused by jamming, angling, jiggling, or banging the little power plug, or yanking the cord while it was attached to the Paperwhite (i.e. same as any other slim electronic device). With the charging cable NOT connected to power, plug in the little plug and very gently check if the charging socket is loose or angled. If loose, it's broken and would probably cost you as much to get it fixed somewhere as to buy a new on (they are on sale for Valentine's day). If the charging socket is NOT loose but is angled oddly, you could VERY GENTLY try straightening it with the little plug. If you are able to straighten it, try charging the Paperwhite and try powering it on or doing the reset I first described. WARNING - you could also break the power socket trying this but I was able to recover my Paperwhite this way after I accidentally caught the cable on a chair back when I was charging it.