The camera comes on, then shuts down. Even when it has new batteries.

Is the lens not coming out at all? did you check is the lens is blocked somehow?
When a mechanical problem occurs, this can be a trigger for the camera to shut down, before something becomes (more) damaged. Did something happen the last time you used the camera?
Was the camera switched of for a very long time?

You probably set the auto power-off for energy saving

I recommend to all my customers with AA battery life issues to try Energizer Lithium AA's. Virtually all battery issues solved. I think alkaline batteries are being manufactured poorly, these days, so even brand new they aren't great.

You're using the wrong batteries. You need to purchase lithium batteries. They are quality batteries for high powered, battery operated electronics. Personally, I have a battery charger and use rechargable duracell batteries. (HR6/ DC1500/ NiMH/ 1,2V) Gives you approximately 16 hrs before having to recharge.

What type of batteries are you using .... is there any thing shown on the LCD ...like the battery low indicator when it shuts down

i had that problem with another camera i toggled with the lens it went in and works like a charm. Dont be to gentile it will go in

a well known problem , this camera eats batteries there are high power (2950MaH) accus , those should be used with this camera even with 2700 MaH it is empty real quick

I've been having problems with the batteries and the camera refusing to start even with fresh batteries. I bought loads of new rechargable batteries and have finally found some that work. Duracell rechargables. Theyr'e brilliant and keep their charge for ages despite continuous use of the camera! Last summer I managed to take 975 photos before the batteries finally decided to give up!

the 3 beeping sound means that the camera has low battery capacity. the lens is stuck out because there is incorrect battery connection. there is an option on the camera setting for the battery type. try this one:
-turn the camera on
-click on Menu button
-select options using left/right, up/down button
-select Set up 2
-Select Battery type
-Select Alkaline for non-rechargable
or Ni-MH for rechargable
-click OK button

this setting should be done when using camera for the first time and whenever you are switching battery types, from rechargable to non-rechargable and vice versa.

I think I Had that problem too. mine also quite suddenly started showing low battery even on new ones... it seemed better with non-rechargeable types. Now the reason I'm on this site is as the lens doesn't open.