Note, the Nikon Coolpix S01 does not have a removable memory card. The memory is built in and this formatting error seems to be a common issue with this camera. There is a small reset button under the bottom cover where you plug in the USB data charging cable however pressing this button does not fix the issue that the OP is having.

I was able to get a 'stuck' S01 working by downloading Nikon's View and Capture NX software to my Mac and opening Nikon transfer 2 where I discovered a photo in memory. I downloaded and then erased this picture which appears to be corrupted and this allowed the camera to restart normally.

Then went through the Home screen to settings where I was able to successfully reformat the internal memory. It is entirely possible that hitting the reset button did help to some extent however once the camera was plugged into the computer and this image removed things seem to be working again.

Of note to the other techs answering this question the Coolpix S01 has 9GB of built in non removable memory used to store images, also the battery is built in. There are no user serviceable or removable parts to this camera, only the proprietary USB connection hiding under the cover on the bottom of the camera that terminates in a standard USB plug which can be attached to your charger or computer.

On a Mac the camera does not show up as a logical drive, it is only accessible through Nikon's software which is free to download from their website here, http://downloadcenter.nikonimglib.com/en/products/224/COOLPIX_S01.html