That sounds odd, but I suspect it is a matter of power availability, since a digital camera uses far more power when actually taking the picture, than at any other time.
When the additional battery pack is not attached, are you perhaps using older batteries? If they are over a year old, then you might possibly have a battery/batteries that are getting weak. Rechargeable batteries do get weaker with time, and eventually fail to deliver enough power to start up a device like a digital camera; they then need replacing. The replacement battery needs to be charged up for 6+ hours before its first use, owing to its having been on a shelf for a considerable time.
Also, you might try cleaning the terminals in the battery compartment, after removing the batteries, first by rubbing off with a fresh pencil eraser, then by wiping the terminals off with cotton swabs moistened in rubbing alcohol, then letting them dry off for 5+ minutes with the battery compartment door open, then try turning the camera On again.
I hope that this helps! Please let me know, if you need further help or have any comments or thoughts on this.