Skyrim requires some sort of audio card or chipset in order to run. Depending on how long it's going to be before you get your new PC, you may want to consider trying a USB sound card. Here's a couple of cheap ones from Newegg -
http://www.newegg.com/Product/Product.aspx?gclid=CLezxvmw67sCFWJo7Aodng0AiQ&Item=N82E16812186046&nm_mc=KNC-GoogleAdwords&cm_mmc=KNC-GoogleAdwords-_-pla-_-USB+Converters-_-N82E16812186046&ef_id=UsuWfQAAAfymlSMW:20140107055802:s
http://www.newegg.com/Product/Product.aspx?gclid=COfTioOx67sCFeJF7AodhXgAOg&Item=N82E16812156032&nm_mc=KNC-GoogleAdwords&cm_mmc=KNC-GoogleAdwords-_-pla-_-USB+Converters-_-N82E16812156032&ef_id=UsuWfQAAAfymlSMW:20140107055822:s
It may not be the best sound quality, but these run around ten bucks each, and one of them may let you limp along for the time being.