The phone suddenly reported “Battery cannot be charged. You must use a Sony Ericsson battery” with an almost new Sony Ericsson battery installed. The status indications for signal and battery levels were both totally low.
I fixed this problem using a software update tool from Sony Ericsson’s website called “Update Service”. This program for Windows is able to update the firmware on the phone without turning on the phone. If you try to turn on the phone it will act really weird unless you select flight mode.
I had to press and hold down the C key before I connected the USB cable to my PC. Then the program handles everything automatically. Conclusion: The battery is still okay, but the firmware went haywire.