Swissgear rechargable lantern won't light up, even though the green led light indicates it is fully charged

There are several different models of the Swiss Gear rechargeable lantern. On most though, you can remove the top portion of the lantern and check the lighting element inside. In most cases the elements can be removed and replaced. I have a dual filament lantern and from experience I know that every so often you may have to go buy a replacement light piece. If the lantern has been bumped or even just strapped to the outside of the pack while walking, it's possible for those elements to become loose and need repositioning or replacement so do check that. I'm sure that it should be unlikely your charger is malfunctioning unless you left it plugged in for some very extended period of time, in which case I would say the light would be more likely to burn out. But definitely try that and if that doesn't work the battery pack on the lantern itself may have an issue in which case you can always get a replacement.