Thinkpad SL500 sometimes won't charge

[WageSlaveEscapist]

Hi, I have an old SL500 that's been through some battles. The issue happens once a month or so, usually when I let it run fully out of battery power. I plug it in and it won't charge, just says battery is dead. I tried the trick of taking out the battery and power cord, then holding the power button for a minute, doesn't work. It kind of baffles me because it is so random and unable to be reproduced or fixed, until I let it sit for a day or two and voila. The power connector wiggles btw. I suspect that there is a loose connection somewhere in the power supply or the connection from the cord to the power supply to the motherboard. Would someone please help me?