If the camera does not work when it is turned on, check to see if the battery is charged. Plug in the Camera and allow the battery to charge for a few minutes, then try to turn the device on. If the camera still does not turn on, this could be a sign that you have a malfunctioning battery. If you have a malfunctioning battery, you can replace it using the Battery Replacement Guide for the device. Source: Fujifilm X100T Troubleshooting

If the battery doesn't charge when it is plugged into the charger, it could be a sign that the battery is not inside the device properly. Check to see that the battery is completely in the device, and try to charge it again. If the battery still does not charge when it is put into the charger, this could be a sign that the battery is malfunctioning. You might have to replace the device's battery, using a Battery Replacement Guide. Source: Fujifilm X100T Troubleshooting

If your pictures are coming out blurry, the lens might be smudged. If the lens is smudged, wipe the lens with a "soft microfiber cloth" until the smudges are no longer present. Alternatively, if the camera is moved while it is taking a picture, the resulting picture could end up blurry, so make sure your hand is stable when taking a picture. Source: Fujifilm X100T Troubleshooting