Studio 1557 can only be turned on with the AC adapter connected, battery is fine - need help

Hi, I've got a Studio 1557 that's working fine except for this issue. After sitting in standby, with or without the AC adapter connected, it will not power up unless the AC adapter is connected. It will do it about 50/50, sometimes it's fine, other times it's not. After the AC adapter is connected, it powers up and I can disconnect the adapter right away and it will keep running on the battery for 2-3 hours. Whenever the issue occurs, both the battery light and the power button light go out, and when I press the power button then the battery light begins to flicker, as if the battery is dead. But it's clearly not dead, as the battery indicator shows full, and if I start the laptop using the adapter and disconnect it, it keeps running for hours. Once the issue occurs, the only way to turn the computer on is to connect the power supply. Removing the battery and attaching it back has no effect, and I don't have a second battery to try.

Any ideas? Has anyone seen this before? I'm thinking the battery circuit board is to blame, but would like to hear other ideas.

Thanks!