Defintely getting power, but not switching on.
There are several possibilities. Let's start with the easiest two. First the battery, take it out and try starting up only with the power supply. Then the memory chips. If a memory chip fails it can cause a no start in IBM's. Take the memory out and try it. Then try it, putting them in one at a time. If these don't work, then I'm afraid your problem lies within. Namingly the power management chip on the motherboard. The pm chip controls the power input, and allows such functions as switching between battery and AC, and battery charging. The pm chip can go without warning, and just because it lights and shows charging doesn't mean this chip hasn't malfunctioned. I've had several IBM's come through my shop that have experienced the same problem you're describing. I've also had them with problems like; it will only power with the battery, won't charge the battery, will charge battery and only run with battery shuts down while charging, only power under AC, etc... all pm chip related issues. Unfortunately, the only solution is motherboard replacement.