Macbook Air only works when plugged in. Shows 'charging' lightning bolt, but battery percentage stays at 4%. Dies as soon as it's unplugged.

The little light on the charger isn't illuminating. Started suddenly yesterday and now as soon as I unplug the mac it dies. Plug it back in and it'll say 'charging' at anywhere from 1'5%, but the percentage never actually grows.

Is there a way to determine if it's the charger or the battery that's being problematic?