For about two weeks I was experiencing problems with charging battery on my Sony Vaio PCG-Z1XMP.

The system tray battery indicator kept constantly changing between charging / not charging. About every 30 seconds. Recently the icon settled at charging, but the battery level stays at 0% and won't go up.

Battery Characteristics from PowerPanel:

Manufacturer: Sony Corp.
Battery Name: PCGA-BP2V
Chemistry: Li-ion
Charge Cycles: 362
Remaining Capacity: 0.00 Wh
Full Charge Capacity: 37.65 Wh
Design Capacity: 48.84

Please advise whether the problem is with the battery, power supply or anything else.

Many thanks
Boris