Frustration of the dead batteries.

So here's the thing.
I am trying to take pictures with my digital camera and it turns itself off because of dead batteries. Fair enough. I put fresh batteries in. Still nothing. The camera tells me the batteries are flat. Ok... maybe these are old ones that I have mistaken for new ones so I go to the shop to buy a new set of batteries. I take them out of the packaging and put them into my camera. And what happens??
The camera turns on for a second, then shuts off telling me the batteries are dead!!

AAAARRRGGGHHHH!

This is beyond frustrating.
I don't know what to do now.

Any suggestions?