Lithium batteries degrade over time; how much depends on what temperatures it’s faced. In normal use, 2–3 years of just being exposed to oxygen will take away nearly half the capacity. And hot-running electronics like laptops and smartphones that put the battery right near a heat source tend to degrade considerably faster. It’s possible that the battery is just shot. For some reason, some laptops won’t start even when hooked to a wall outlet unless the battery is present and has at least a small charge.
Of course, it’s possible that you just aren’t charging. Power plugs are delicate things, some more than others, and I’ve seen more than a few (mostly on older laptops) knocked loose. I don’t know about your particular laptop, but whenever mine is plugged in, it lights up two LEDs on the front even when it’s not running. Most laptops I’ve seen are similar; one LED will light up green to indicate power from an adapter and another will be yellow or green to indicate whether the battery is fully charged or not.
While it is possible that the power adapter is toast, I have to say that I personally have never seen that. My experience is that it’s usually either the battery or the power plug getting ripped off the motherboard.
@longgone Heat kills lithium-based batteries like the ones in most electronics these days, and also softens solder enough to possibly de-mount some components from a circuit board. You’d be better off cleaning it out so that the heatsinks can do their job. Running a computer with lint in the heatsinks isn’t much better than running a car with no coolant in the radiator. A can of compressed air would do you a lot of good.