Skype is resource heavy and a pain to deal with I will help you though any questions you might have. so feel free to post again, i know if you follow the instructions below it will clear up any issuse you might have.
You have to trick the computer. Download skype install it and then go to add/remove and uninstall skype. I know this seems backwards but installing/uninstalling will let the application show up in add/remove.AFTER YOU UNINSTALL REBOOT AND SKYPE SHOULD BE GONE.sometimes what happens especially with skype which seems to have services running even after uninstall or a previus installs
1: install skype
3:go to add remove and uninstall
4:reboot it should be gone