Okay, let's try some simple repair routines and see where that takes us.
This will require some restarts so please bookmark this so that you can get back to me with the results.
I want you to repair the permissions to begin with, this PDF will explain how.
After that I want you to do a pram reset, this clears the machine and refreshes it.
To do a PRAM reset, you need to restart your machine and hold down these 4 keys.
‘Option’, ‘Command (Cloverleaf or Apple)’, ‘R’ and 'P'.
Keep them down until you hear 4 startup chimes, this is the sound that your Mac makes at startup.
If you have a wireless keyboard then the procedure is a little bit different.
Use the very same keys but wait until the first chime and immediately press and hold those keys. I recommend getting your fingers ready because timing is critical.
This resets all of the system buses on your computer, USB, FireWire, display, ethernet and your keyboard/mouse/trackpad.
This will correct many faults but not necessarily yours.
Then after that is a safe boot, this runs some UNIX repair routines that normally get neglected.
To do a Safe Boot, restart and before the first chime press and hold the 'Shift' key.
Wait until you see the Apple logo and the spinning gear appear, then let go.
It can take as long as 20 minutes to load, so please be patient.
When the login screen appears it will say in red on the login window 'SafeBoot'.
Now login and give it a few more minutes to finish loading.
Then restart normally.
If the problem persists then restart normally also, other fixes will need to be done.
After you do these things try Skype again, if it works then the problem is solved, if it does not then we will move on to other things.
Please let me know.