G'day and welcome to thinkpads.com!
Not sure where the lid switch is positioned and what type of technology is used on the SL500 (younger daughter currently has one in her possession) but that could be a source of your problem. There could also be a blown fuse on the motherboard. These two things are based upon how previous Thinkpads were designed.
The older systems (before the '60 series) used a mechanical microswitch mounted on the motherboard (or sub-card), typically activated by a plunger/post located somewhere near the back edge of the keyboard bezel. There would be a matching "nub" of plastic located on the LCD bezel which will push down upon the switch when the lid is closed. Newer Thinkpad systems will use a switch controlled by a magnet (a Hall-effect switch). That switch could either be mounted in the lid assembly (usually on the inverter board itself) or in the base. The magnet would be in the opposite location. So, if you don't see any obvious signs of a mechanical switch, try dangling a small steel chain across the bottom edge of the LCD bezel and along the back edge of the keyboard bezel and see if it sticks. If it does, that will tell you there's a magnet there but not really say anything about the correct functioning of the Hall-effect switch. Since the switch is supposed to turn "off" (cut power to the inverter) only in the presence of a magnetic field, I would guess
that it would not fail such that it's always "off".
It's known for many of the older systems to have a fuse on the motherboard which protects the power going to the inverter. They are usually located on the board near the connector for the LCD ribbon cable. You would need an ohmmeter to check it and the Hardware Maintenance Manual for the procedure to tear down the system:http://www-307.ibm.com/pc/support/site. ... 69929.html