You have to set the time and date every time you

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According to the review features of Sony Cyber-shot DSC-T10 Digital Camera, this camera doesn't have a feature for superimposing date/time on images, however you can print images with the date superimposed, So by default u cannot put the time or date stamp on your images, but after taken the images you can manually put the stamp and can print the images.
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If you have forgotten to set date and time then you can also set date and time after turned on the camera. to set date and time follow the given instructions:

• Press the Menu button on the rear of the device, then choose Set with left or right button, Then go to Setup menu.
  
• Select Option followed by time icon. This brings up the date display. The display blinks as it has not yet been set.
• With the help of Right or left buttons select Year, Month, Day,Hour or Minute. Then press Menu/Ok button after the settings completed. Now every picture captured with the Fujifilm FinePix F460 will save the date and time to the pictures

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have you check the settings for time and date have you saved it? You can also try to remove the cam battry for 2 mins. then put it back in then turn on the camera and then after few secs. turn it off, then see if the issue persist.

You may want to set the factory defaults by going into the main maenu.

There is a button battery in your camera (CR1220) that remembers the date and other settings when you remove the main batteries. It probably needs to be replaced. It's in a slide-out holder next to the AA batteries (see page 184 in the manual).

You turn on the date stamp by using the photo size settings. Press the Function key and scroll down to the bottom item (usually L). Then scroll over to the Date Stamp icon (to the right of the L, M1, M2, M3, S options). Press the Function/Set key again.

to keep the date on, you have to leave the camera off with a charged battery for 24 hous to charge the inner battery that keeps date on. If this doesn´t solve the problem then is because the inner battery won´t charge anymore, but it will take pictures as normal without the date. To avoid this don´t leave the camera too long without use or with a worn battery.

Turn camera ON lens will come ON
Press Menu scroll far right,
Keep scrolling down untill you get to Time and date.
Press Zoom and read help menu.
Set time and date and functions.

Vitally

The date and time settings are displayed after turning on the camera. Solution
It is normal for the camera to lose time and date settings if the internal battery is left uncharged for an extended period of time; some cameras will default to the time-setting screen when turned on if this happens. Follow the steps below to resolve this issue.

1. Turn off the camera.
2. Do one of the following:
   • Insert a fully-charged battery pack into the camera.
   • If the camera is supplied with an AC power adapter, plug the adapter into a working electrical outlet and then connect it to the camera.
3. Allow the internal battery that retains the time and date information to charge for at least 90 minutes.
4. After enough time has elapsed to sufficiently charge the internal battery, turn on the camera.
5. Set the time and date.
6. Turn off the camera for 30 seconds.
7. Turn on the camera again.
8. Check to see if the date and time have been saved.

The troubleshooting steps listed above should resolve your issue. If you have completed all of the steps and the issue is not resolved, service may be required. The Sony® eService Web site at http://eservice.sony.com/ can assist you in obtaining service from a Sony Service Center or locating a Sony Authorized Servicer.

Try resetting your camera. In picture taking mode press menu. Go to setup, go up to reset, press right arrow, make sure reset is highlighted and press set.

Then TAKE OUT MEMORY CARD. Go back into menu, go to setup, go up to format, press right arrow and highlight format, press set. Input ur date and time again and then power off and back on. If that doesn't help then you have to send into repairs. 800-706-2534 and keep choosing option 2 and they will tell you where to send it.

Possible solution?

PROCEDURE
1. Initialize the system.
a) Enter the TEST mode.
b) Select "3:ROM UPDATE" and press SET button.
c) Next, select "5:SYSTEM INITIAL" and press SET button.
d) The following message appears.
SYSTEM INITIALIZE
START ...
PUSH OK KEY?
e) Press SET button and System is initialized.
"SUCCESS !" appears on the monitor.
2. Write firmware.
Update the firmware version"
Write the firmware.
If the TEST mode boots automatically, change "USB TCC ON" to "USB TCC OFF".