Try booting it with no main battery inside. A dead main battery will (sometimes? always?) prevent booting. The dead coin-cell backup battery would not normally prevent booting, but might cause other anomalies once you get it running. As equill says in the posts above, however, they will often revive with some TLC.
Opening a PB1xx up is not difficult; these models are easy to work on. Just be careful at the beginning when separating the top from the bottom, as there is a delicate cable that connects the two halves which requires disconnecting right at the beginning. You do not want to tear it.
When apart, check to see that processor and ram card (if installed) are a) present and B) properly seated. It is a good idea to disconnect and then reconnect all plugs, which sometimes has the effect of renewing old and tired connections. Also check to see that the internal power connector does not require re-soldering.
If these simple strategems (which should not take you more than 15-20 mins.) do not lead to success, then the next step would undoubtedly be to verify that your power adapter is providing current to the machine.
Opening a PB1xx up is not difficult; these models are easy to work on. Just be careful at the beginning when separating the top from the bottom, as there is a delicate cable that connects the two halves which requires disconnecting right at the beginning. You do not want to tear it.
When apart, check to see that processor and ram card (if installed) are a) present and B) properly seated. It is a good idea to disconnect and then reconnect all plugs, which sometimes has the effect of renewing old and tired connections. Also check to see that the internal power connector does not require re-soldering.
If these simple strategems (which should not take you more than 15-20 mins.) do not lead to success, then the next step would undoubtedly be to verify that your power adapter is providing current to the machine.