Hi Frank,
Thanks for posting your query in Microsoft Community Forums.
I understand that you are unable to find Internet Explorer icon on Desktop and Start Screen. Also, you are unable to open Internet Options in the Control Panel.
Please answer the following questions for better understanding of the issue:
1) What were the recent changes made to the computer prior to the issue?
I would suggest you to perform the methods suggested below:
Method 1: Open Internet Explorer from Run Window
a) Press Windows key + R (opens the Run window)
b) Type "iexplore.exe" and press Enter.
Now if you are able to open Internet Explorer then follow Method 2
Method 2: Alternative steps to create a shortcut to Internet Explorer
1) Carefully select and then copy the following command:
"%programfiles%\internet explorer\iexplore.exe"
Important Make sure that you select the quotation marks (“) at the beginning and end of this command.
2) Right-click a blank space on your desktop, point to New, and then click Shortcut.
3) In the Create Shortcut Wizard, right-click the Type the location of the item box, and then click Paste to paste the command that you copied in step 1.
4) Click Next.
5) In the Type a name for this shortcut box, type Internet Explorer.
6) Click Finish.
A shortcut to Internet Explorer is created on your desktop. You can double-click this icon to open your home page in Internet Explorer.
Method 3: Remove and re-add the Internet Explorer from Add remove feature
Refer to the link: http://windows.microsoft.com/en-US/windows-8/turn-windows-features-on-off
Hope the above information helps you resolving your query, if you have any query related to Windows feel free to post. I will be glad to help you.
Thanks & Regards!