Dell Inspiron N5110 does not work when powered by battery only even though it showed battery was installed and charged.

There were two metal clips on battery connector inside Dell laptop which were held in place by spring force. If they wiggled free and fallen inside the computer (as shown), it might short circuit some functions, very likely the battery.

They can be seem by removing the memory modules. It is better to keep them out.
D5110 Battery Connector Clip Off Position
D5110 Battery Connector Clips