If Skype will not install then try this work around using the portable version

I tried uninstalling Skype which completed successfully but it was still installed on the computer so therefore I could not update to a later version of Skype.

 

In the end I installed the Skype Portable version 7.2.0.103 and this allowed me to use Skype again. I installed it on my PC and it can also be installed on a USB drive if required.

Download Link:

Skype Portable Version 7.2.0.103 (Allows you to install on PC or on USB Dongle)

 

I tried the following steps and still had no luck. They may work for you so have kept the details noted below:

I uninstalled Skype by going to the following on Windows 7:

Start > Control Panel > Programs & Features > Then clicking on Skype and clicking the “Uninstall/Change” button and choosing uninstall.

I completed this step and Skype was no longer appearing on the Programs & Features list but it was still installed.

I then had to do the following:

First, uninstall Skype again then have a look in C:\Users>{yourname}>AppData for any Skype folders which might be clinging on to settings you want to bin. Also, hit Windows key and R together then type regedit into the Open box an hit Enter. Navigate to HKEY_LOCAL_MACHINE>Software>Skype and delete the entire key then click Edit and Find, type in Skype and delete any further references you find by hitting Function 3 to find the next one every time. Leave the Registry by the File menu Exit and restart the computer twice. That should do it

If you try to install a newer Skype version and get this error message:

Installing Skype failed; code 1638

After spending hours on attempting to get this to work I gave up as it was not a high priority for me when Skype Portable works fine.

 

Ref:
http://www.tomshardware.co.uk/forum/8743-63-totally-delete-skype-windows