if the charging light does not come on when it is plugged in, then it is not charging.
I am concerned that you may be plugging it into an incompatible AC adapter. Do the 5500 and 5600 use the same adapter normally?
also make sure that you unplug all cards, and everything else that might use any power.
do a "hard reset" by just pressing the reset button inside the battery compartment, those keys are not for this situation. I think they are for changing ROMs.
after the reset, then put the battery in and start charging. If the charging light does not come on, it is new battery time. If the light does come on, let it charge like 16-20 hours to let the backup charge as well.
I do have a blog post about when this happened on my collie, light did not come on unless I followed all the steps, even with a new battery:
http://sdjf.wordpress.com/2008/06/21/batterysdjf