I recently bought a DMC-TZ3 and have been researching memory cards. Several sites sell cards with the camera and list the card type. I would suggest buying one of these cards. Any cards larger than 2gb must be SDHC type SD cards. There appear to different types of SDHC cards, 1.0, 1.1 and 2.0. Check out Wikipedia.org for a description. 2.0 cards are not compatable for devices developed prior to 2.0 so that may be the reason for the camera problem. So far I haven't seen anything that states what type SDHC card the camera requires. I found a computer memory site that that sells memory that they say will work. There may be others.
http://www.mymemory.co.uk/compatible-memory/Digital_Cameras/Panasonic/Panasonic_Lumix_DMC-TZ3
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