Latitude 5420 Power Issues

I went on a short vacation to California a week or so ago, during which (after a flight) my laptop was acting strangely (slow to boot, or issues with the display/keyboard). When I had gotten back from my vacation (only about 3-ish days), it was entirely unresponsive and has only gone so far as to light up the caps lock or battery buttons alongside the battery LED that shows the battery state.

I can't boot the computer at all, no display shows and no inputs are detected at all (nothing lights up). I've tried all sorts of things like D+Power or holding down the power button for 30 seconds. Only recently I've seen that the battery light illuminates while plugged in and I'm holding the power button (and under no other circumstance), showing a signal for "critically low power", which never actually changes despite charging it. I've opened it up via the back plate to see if something was disconnected or anything, but nothing's burnt out (to my knowledge), and the battery seems fine.

Is it able to be saved, and if so, how?