Will not switch on with new batteries
I wonder what batteries you use? The best would be two AA rechargeable NiMH batteries. But a new CR-V3 lithium battery should work also.
When you have rechargeable batteries, you should check if they are charged. And when inserting, check if you did out them in correct. Only the CR-V3 is protected for inserting it wrong. when you have two batteries, you can put them in the wrong way. Then, if you did not use the camera for a long time, please make sure all contacts in the battery compartment are clean and shiny. If not, try to clean them, with a clean cloth. Never use anything sharp in or close to a camera. Contacts, could be rubbed with a little electronic contact oil, but the oil must be removed afterwards. As strange as it may sound, even the contact oil can be cause of oxidation on contacts.
When the batteries are in, make sure the battery door is correctly closed.
If you checked everything and you are sure the batteries are in correct, just try switching on and of several times, by opening and closing the lens barrier. Also while the lens barrios is closed, press the play back button on the back side of the camera. If both don't work, then again the batteries are under suspicion.