The batteries I put in my camera are discharged very quickly, usually after only a few shots, even when the camera is off. Is there a short circuit, or something like this, that I have to investigate?

SOURCE: camera batteries drain quickly

Open the battery door and check the contact between the camera and the batteries. Most often then not there is just a bad contact and it's ruinning your baterry life.
Make sure that the contact are well placed and that there is no rust or dirt build up around there.

SOURCE: going through batteries abnormally quickly

Hi. I had the same problem with my Canon S1 IS. In my case the problem was caused by flash capacitor. To check if it is the case just follow the following procedure. 1. Turn on the camera. 2. Be sure that low battery warning is flashing on LCD. 3. Turn off the flash by pressing flash button (be sure that flash is OFF but not in AUTO regime). 4. Turn off the camera. 5. Open and close the battery door. 6. Turn on the camera. 7. Take several pictures.
If after these operations the low battery warning does not show up it means that flash capacitor causes the problem and it should be replaced. Or you still can make pictures with your camera without using a flash.

SOURCE: Batteries fail in very short time

I had the same problem but I fixed it by buying 2 rechargable CRV3 batteries and the charger. At the time such batteries were not common, so although I got a brand that I never heard of (CTA) and they have been great, They last a long time and power is no longer an issue.

SOURCE: SONY DSC CYBER SHOT

Try clean contacts of camera for battery and contacts of the battery also, specially the middle one - it is for communication between camera and circuit inside the battery. If the problem persists, try use another battery in your camera, or your battery in other compatible product - you determine this way if the problem is inside the battery (I hope, it is cheaper) or inside the camera.

SOURCE: quick Battery Discharge on LG KU990 Camera/Phone

My problem turned out to be self inflicted as I am a new user of this phone and found out it was purely "Finger Trouble" my phone had closed down and I could not bring it back to life and found that by connecting the battery charger whilst charging I was then able to operate the phone through the charger and from thence on after disconnecting the charger the phone returned to full use. Sorry to have bothered you but grateful of your offer of assistance, I shall know where to go if something more serious should arise. I am a "Silver Computer User" of 80 tender years trying to keep up with the 21st century so that's my excuse for getting in a mess with my first Mobile Phone/Camera. Regards & Thanks Again, Dennis Sparrow