My Kodak EasyShare M340 turns on, but then shuts off immediately.

There is a lot of advice I can give you mostly pertaining to the lens mechanism, but If it's a few months old , I would take it in as it probably is covered by a 2 year warranty depending on where you live.

Nevertheless , here are a few steps you could try if no warranty if applicable :

The problem is either something is jamming the lens , or that the lens sensor is faulty. This is a very , if not the most common problem with modern digital camera's.

Most of the time the problem is that sand , dirt and grit gets lodged in the camera lens barrel thus keeping it from extending properly but could also be caused by a drop or a hard knock on the camera.

Firstly , the odds are not with you on a DIY fix so don't be disappointed when the following steps do not work.Nevertheless , some people have fixed their camera's using the following steps.

Use these at own risk as it may further damage the camera.

Firstly try charging your batteries overnight and then try the camera again tomorrow.
Try connecting your ac adapter or usb cable.
Try holding the shutter button while switching on the camera.

These 3 options provide your camera with more power available to the extension mechanism which could overcome some of the particles that could be lodged in there if there are any.

Try using compressed air (best is a clean air can bought at a electronics store) and blow between the lens and the casing. This should help dislodge some of the particles.

Look at the lens , and if some of the lens 'circles' are misaligned or not concentric then try wiggling it (while holding camera lens down) so that some of the particles can escape. Also try moving the lens away from the side with the biggest gap (also upside down)

Try gently pushing or pulling the lens when it tries to extend but this is risky as it may cause the lens barrel to slip out of its guidance system.

Another way to do this is to place the camera lens down on a hard surface and then power it up. Be sure to use a soft cloth or something similar as to not scratch your lens or casing. Let the lens push the camera up and down a few times and sometimes the little resistance provided by the camera is enough to get things going again.

As a last resort if you decide to replace the camera try hitting the camera near the lens with increasing force with the palm of your hand. Between each hit , try using it again.

Other than that , I would take the camera to a repair center for a evaluation to see if it would cost more to repair than to replace the camera.

I think Kodak charges about $100 flat rate to repair this error. If it is still under warranty I would suggest you take it in before trying any of these steps and remove any off-brand batteries or accessories as some stores are really fussy about warranty repairs on camera's with non-brand accessories.

Hope the advise works. Good luck and don't hesitate to contact me if you need further assistance or information.

Regards
Stephan