How do I know which component is failing in my laptops power system? (i.e. battery, charger, power supply)

For the past week or so, when I plug my laptop into the wall it only “registers” that it is being charged about 30% of the time. The rest of the time it continues as if it were on battery power and dies rathr quickly. Is this an indication that my battery itself is going bad or that it’s the charger? I’ve also heard that there is a component inside the laptop called the “power supply”. The bottom line is that I am looking for the least expensive way to fix the problem… but don’t know which component to address. Any words of wisdom from the fluther crowd?