Most likely it's bad caps, as other people have said.
However, there are many hard-power Macs (usually '030 or '040-based) that refuse to boot properly without a good PRAM battery. I learned to jump some of mine, either via the reset button (if available) or a quick power cycling.
Later models with both soft power and hard power switches (typically AIO models, like the LC 520) may need to sit plugged in with the hard switch turned on for a day or two before they'll power up via the keyboard power button, regardless of the PRAM battery. Equill helped me with that tip when my new Mac TV wouldn't turn on.