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Do you happen to have the camera connected to a computer when this happens?
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Thanks for the response. To ensure that we have a known group of settings for the camera I would like you to perform a soft reset of the camera. To do this, with the camera powered on, press both the AF and the +/- buttons at the same time and hold for about 5 seconds. You should see the LCD flash to let you know that this is complete. Once this is done, remove the battery, memory card, lens, and any other accessories that you may have connected to the computer and let it sit for a few minutes. Then re-install a freshly charged battery only and check to see if the access light is still flashing an whether or not it runs the battery down. This will allow us to isolate the issue to either the camera body itself, or one of the accessories connected to the camera.
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The next thing to try is checking the memory card slot to see if there's a bent or broken pin in the slot that is causing the access light to stay on all the time. Shine a flashlight into the empty card slot and see if you can see any pins that look out of place. The only other thing other than a bent or broken pin would be the USB port on the camera. It seems that the camera thinks it's connected to a computer or either the card is set for a transfer all of the time.