Screen wont work and when you shoot it says its "Busy"

Question edited for clarity.

It sounds like your battery has failed or have you tried two of them? Is there a date on the battery? They don't last forever. Check the charger for output using a digital multimeter. Also try cleaning the battery contacts on the battery and in the camera.

https://www.google.com/search?q=olympus+t100+battery

Powered with a LI-80B Lithium-ion battery (recharged via the included AC adapter) you can enjoy shooting the T-100 for about 190 photos per full battery charge.

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Taking out the battery, when a camera acts strange, is a good thing ONLY. be sure the camera is not busy saving pictures, because you could damage all pictures on the memory card.
I'm not sure the lens was out, when it was connected to the computer. Let us assume it was. Normally, the battery should be charged when the camera is connected to a USB connector on the PC. But not all USB connectors are perfect wired. And if you use a USB hub you can be sure the battery was not loaded. So as soon as the camera came from the PC it needed full power and could not get it.
Now you removed the battery, but before placing it back in the camera, please charge it on an external charger. When you place the charged battery, and the yellow light starts flashing again and won't stop quick, you could try to reconnect the camera to the computer and see what that brings. I would have switched off the camera, before I disconnected it from my PC.

Than the sand issue. If just a grain of sand is in the lens bellow, it could serious obstruct the lens from going back. If you can see the grain of sand, you could try to get it out. Very thin needle (or two?)
But if you can't see something, don't move the lens at all.
You could damage the gears in the focus and zoom mechanism.
I wish you luck with the camera.

First, make sure it is set to continuous shooting.

Second, if you get a busy message, your buffer is probably full. This is a limitation of the hardware, and there might not be much you can do about it.

sometimes camera will not turn on. battery charged but does not function???

Please make sure to check if the battery is fully charged. Second, check the menu option for battery saving mode and turn it off. If the battery is getting old and not charging fully anymore the priority of the camera is the shooting mode.

The easiest solution, and it worked for me the one time it happened was to remove the battery, let it sit. Reinstall the battery after a few minutes and try it again. make sure the battery is fresh.

Sounds like your memory card is full. Trya newone andsee how it reacts to that. Best wishes!

If the flash fires a full charge(eg. in a dark environment) then this message will appear whilst it recharges. If the message appears all the time and you cannot take a photo there is most likely a problem. Try taking some pictures without the flash card to eliminate that first.

Could be that the battery is weak, and should be replaced as it is not holding a charge.

Causes of memory card corruption

• Turning off a camera before an image is completely written to the memory card.
• Removing the memory card from a camera while an image is being written to the card.
• Removing the card from a memory card reader while files are still being transferred to a computer.
• Batteries conking out as files are being transfered directly from the camera to a computer. Note: always make sure you have fully charged batteries before transferring images.
• Removing the card from a card reader while folders and files from the card are open on a computer.
• Opening, deleting, renaming or moving files on the card while its contents are open on a computer.
• Using a memory card which has not been formatted in the camera. Use the delete/erase function when needed, however a card should be regularly formatted.
• Formatting a card in a computer instead of the camera.
• Inserting a second memory card into a card reader before closing and removing the first when viewing images on the card from a computer.
• Taking photos when camera batteries are nearly empty.
• Taking photos too rapidly so the camera can not complete writing one image before starting the next.
• Continually shooting and deleting, shooting and deleting images when the card is full.
• Letting a memory card get too full before downloading the images to a computer or storage device. Cards that are too full may overwrite the card headers.
• Using a memory card from one camera in a different camera without formatting it in the new camera first.