Error Failed to install Skype
As you can see in the error log, it says that a version of the product is already installed. All you need to do is go to Start -> Control Panel -> Add or Remove programs. Just wait until the list shows and look up Skype.
Removing it will delete all files that could be corrupted and the next install of Skype should run nice. If this does not help, go to Start -> All Programs -> Windows Update.
NOTE: Use this step only if your Windows is Genuine valid.
If opposite, skip this step and stick to the first one. After this, error 1638 should be gone and Skype should work like a charm. Hope this helps.