I decided to power up my neglected 5600 only to find that it will only power up when connected to external power. If I remove the external power the 5600 dies. I have checked the battery by swapping it with my 3100 both the 5600 and 3100 batteries work in the 3100 while both fail in the 5600.
The 5600 was working okay when I last used it so I don't think anything could have physically happened it. Also the 5600 is charging its own battery without any problem.