The fe-280 user manual notes hat it is possible to insert the battery "the wrong way round" in either the charger, or camera itself (whereupon its hard to extract).
An extract from the faq about it .....
The camera no longer powers on. What could be wrong?
The battery may be dead or underpowered.
If the battery is completely drained, the camera will not power on when the Power button is pressed. If the battery is nearly drained, the camera may briefly display a Battery Empty error message and then power off, or it may power on and then quickly power off without displaying the error. In either case, charge the battery using the LI-40C battery charger bundled with the camera.
Be sure to properly align the arrow on the bundled battery with the arrow on the bundled battery charger. It is possible to force the battery into the charger so that the arrows are not aligned. This is an improper orientation, and the battery will not be charged. For instructions on how to properly inset the battery into the charger, please see "How do I charge the lithium-ion battery?"
So in a nutshell, the first few steps to check are:
1) Are you sure the battery is charged correctly?
2) Have you inserted it into the camera body correctly?
3) Do you have a spare charged battery to check the camera with? (A photo store will do this for you sometimes, if you ask nicely).