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First, when you reinstalled Skype did you download the most current version of Skype from the Skype website or did you reinstall an existing version of Skype that you already had available?
Also, click Start, Control Panel, Add or Remove Programs then select Skype and click Remove and uninstall then reboot and after a clean uninstall then install the latest Skype software from download and try the speakers again.
If the above does not resolve the issue then double click on the speaker icon in the lower right corner of your PC desktop then in the window that appears make sure that all audio input and output is set to high volume and that mute is not selected for any of the items. Then click Options, Properties then select your Audio devices then click Playback then select all the options in the list and click Ok then back in the volume control click Options then click Advanced then make sure that all the additional options are set to high volume and that they are not muted then click Ok or close the volume control.