Hi Arbalest,
Thank you for sharing the information.
It appears to be a hardware failure. I would recommend that you try and wiggle the AC adapter cord and check if it charges the battery. Also, you try connecting an alternate good known AC adapter. If it charges the battery, replace the AC Adapter else motherboard replacement may be required.
Please share the results of the system performance if you have tried the steps for optimization and maintenance of Windows Vista.
