Camera turns on, then right back off

yup, your batteries are dead, buy new ones.
Old ones are not holding a charge

Take out the batteries for a while. Insert them again and try to reset your camera to factory settings. If you are using a SD card replace it. If the problem continues your camera need to be serviced.

If the rechargeable battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all. OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time. If the battery drops to an unacceptable charge level then the battery needs to be replaced. Rechargeable batteries will fail if stored in a discharged state for long periods.

It is now over seven years old - if it has been used extensively, it may just be worn out.

switch off, leave it to charge overnight. try again the next morning.

Alkaline batteries just don't have the power for more than a few pictures in today's power hungry digital cameras. Some batteries may also have reached their shelf life at the store, and though brand-new right out of the package may even have problems just powering startup of the camera. The one's that came with your camera are just to show you that the camera works, but as you've discovered, they'll only last for a few pictures. Digital cameras that use AA's for the most part should only be used with modern rechargeable batteries. If you read the camera's instruction manual concerning batteries, you should see the same recommendation.
Modern rechargeable batteries have over 5 times the power density of alkaline batteries (that's right, they last up to 5 times longer than an alkaline battery. And you can recharge them over and over!). Keep in mind rechargeable batteries will save you much money in the long run over alkalines, AND they'll last for at least 100 pictures per charge (and probably many many more). You'll be very pleased with their performance, and may be angry with yourself for not buying them sooner. When at the store, look on the package for a power rating of at least 2500 mah.

That sounds like your battery could be dead/not hold a charge. If you've charged your battery already and your camera still won't stay off and turns off right away, it's time to purchase a new battery for your Samsung TL105.

You can purchase replacement batteries quite cheap here:
http://www.amazon.com/Samsung-Digital-Camera-BP70A-Battery/dp/B003OEDQBE

Your camera is 20+ years old. They are electronic and most likely it is dead. Clean your battery contacts. If that does not do it... again it's a 20+ year old camera. The electronics go, just like a dead tablet or computer, a bad transistor will kill the camera. You can buy used Rebels for dirt cheap, under $50. But again, you are buying an old camera.

I know you mean your kodak easyshare camera battery life is over,and the new kodak battery replacement you buy isn't effective to you camera, it may be a compatibility problem,You should have take your camera with you to test if it is fit.Now you can get some kadak battery information or get from Inernet search engine.

If the troubleshooting section in the back of the user guide doesn't help, I sugget getting in touch with Sony and asking them if it's normal, the only thing I can suggest in the meantime, is taking the battery out while it's not in use, or recharge it a few hours before you're due to use it. Phones get like it after a few years and with technology advancing the way it is these days, you'd expect a battery life lasting longer than a week, not a day.

Things to consider:
1. When it's off, is it off or left on standby?
2. Where did you buy both the camera and batteries from?
3. When you charge it up, do you charge it up with a half charged battery or a totally dead battery?