My camera does not turn on it is brand new what can it be?

I suggest you return the camera to the shop where you bought the camera for a replacement or warranty repair. If you try to fix it yourself you may void your warranty.

As its brand new, I'd go straight back to the shop with it. You've got an automatic 1 year guarantee with all electrical products bought in the UK

Inside the camera, check the brass contacts where the battery connects to the camera. Clean it with rubbing alcohol (use a cotton swab) and try to turn it on after insterting the battery.

20 to 30 shots on "fresh" batteries! Do you use the flash on all shots. That really drains them. I would try to set the camera to "factory default settings" in case you changed something that is causing a drain. I hope you just bought some bad batteries.

The best thing I EVER bought for my Olympus was the Re-chargeable Lithium Ion batteries. The worst thing I did was buy an off brand. That was a waste. I ended up getting the more expensive brand Olympus recommended and all was GREAT again!! 1,000's of pictures later and they still work great.
Good Luck

is there any plug for AC ? try work with AC. if nothing happens looks like mainboard.

Yes it sounds like you should return it. If you just bought it I would not take the chance, exchange it for another one and see if you run into the same issue. Then go from there. If you need further assistance let me know.
Thank you,
Lee

I bought this model several months ago and it was working great up until Christmas time.  For some reason it just stopped working.  I couldn't get it to turn on OR sometimes it would turn on after several attempts.  I kept changing the batteries and sometimes that would work, but it was more or less random successes.  I found this link on FixYa : http://wwwuk.kodak.com/global/en/service/batteries/batteryDigCamChart.jhtml?camera=C813
I was using generic batteries (Philips) which I bought in bulk from a discount tech store and these batteries were working in the camera since I bought it.  The batteries were new; just generic.  By coincidence I ended up buying KODAK branded alkaline batteries from the same store.  I replaced the older generic ones with the KODAK batteries and the camera came back to life!  I'll leave it off for a day and see if it turns on tomorrow.

Sounds as if it needs a repair but get a quote first as it may be better to purchase new

try looking at the symbols on the battery and then on the camera and try putting them in that way and if that doesnt work try an other brand of batteries

You need to use Nimh battery specifically designed for digital
camera use with high ampacity usage.