Red battery light even with new batteries - then shuts down

Your camera can work with 2 AA sized batteries.
Always charge NiMH batteries before using them for the first time, or if they have not been used for a long period.
Always charge sets of batteries together.
Do not use alkaline batteries unless it is absolutely necessary. In most cases, alkaline batteries may have a shorter service life than NiMH. Alkaline battery performance is limited, especially at low temperatures. The use of NiMH batteries is recommended.
AA manganese (Zinc-Carbon) batteries and NiCd rechargeable batteries cannot be used with this camera.
If you are sure you have good batteries, also check if all contacts are clean and shiny. No oxidation is allowed. To clean contacts never use sharp tools. They can damage the camera forever.
Eventually clean contacts with a cotton swap or a dry cloth.
Also check if no debris is in the battery compartment. Just a little pice of paper can spoil all the (camera) fun.
Just to make sure, try some other batteries, then the ones you are sure of, they are fully charged. Perhaps, next time you are less convinced.