Hi Swathi,
As you have deleted the Screenshots folder, I would suggest you to restore default library settings and check.
Follow these steps to restore library settings.
a. Press Windows key + E to open Windows explorer.
b. Right click on Pictures library and select Properties.
c. Click on Restore Defaults button.
There is no way to find out where the screenshots have got saved.
You can refer to the suggestion given by mike610 on March 29, 2013 in the following thread****and try the steps.
Note: This section, method, or task contains steps that tell you how to modify the registry. However, serious problems might occur if you modify the registry incorrectly. Therefore, make sure that you follow these steps carefully. For added protection, back up the registry before you modify it. Then, you can restore the registry if a problem occurs. Follow these steps to take back up and restore the registry.
a. Go to start screen and type regedit.
b. Select regedit and right click on the screen.
c. Click on Run as administrator.
d. Locate and click the key or subkey that you want to back up.
e. Click the File menu, and then click Export.
f. In the Save in box, select the location where you want to save the backup copy to, and then type a name for the backup file in the File name box.
g. Click Save.
Reference:
Screen Shots in Windows 8 -Rapid Screen Shots
http://support.microsoft.com/kb/2790489/en-us
Let us know about the status of the issue. We would be happy to help you further.