Laptop shuts off when I plug in the charger – hardware or Windows?

Got an Acer Aspire 5. When I plug in the charger, the laptop turns off—sometimes it stays on for a few seconds, then shuts down. It also crashes under light-heavy use. If I unplug it and turn it back on, it works fine. Plug it back in, and it dies again.

Tried booting it while plugged in and got an error screen. Not sure if this is a Windows issue or something hardware-related. Anyone seen this before?