I am trying to use an ethernet cable cord and a ethernet network splitter connector coupler plug for my desktop and laptop. When I plug them both into the coupler my internet gets disconnect. Can I do that or is there something else I need to do.
Thanks

You want to use a "network switch" typically. The most basic ones are quite inexpensive. It allows you to connect a source cable and as many device cables as you wish.

Amazon.com: NEW TP-Link 8-Ports 10/100 Fast Ethernet Internet Network Switch: Electronics (http://www.amazon.com/TP-Link-8-Ports-Ethernet-Internet-Network/dp/B0032GNWK4)

8 Ports 10/100 Mbps Fast Ethernet Network Switch/Hub - N01 - Buy.com (http://www.google.com/product_url?q=http://clickfrom.buy.com/default.asp%3Fadid%3D17902%26sURL%3Dhttp%253A%252F %252Fwww.buy.com%252Fprod%252F8-ports-10-100-mbps-fast-ethernet-network-switch-hub%252Fq%252Flistingid%252F38714672%252Floc%252F1 01%252F210819759.html&fr=ANvAj_qBhBAkJyimifycQxg-3iK-OPLKm3gnR_9xuOWRB4NY4jNjfqhOnTo5kydD7Le12efJhSbV_E w4ELj6M65man8o1p_iX3GBtqXwljnoHsH0oULTokCNRZN1cw8D dRlhMWjCO85OC4C2xtg5wW_Pdt9C255dSFiKuZsoCXg21jcSHs 92izyP77AqKxCN1D8ErCGv10RPJGObAnDzAhGKO89lowZIBrfB rWFIiQwxtLJ8EHKqUoAofPfuO4LApGlOGtOdwETAxPPHesxkVA _HWeWXySekphKVivdaDbaxK7ArDSCFGY2Rq6fPFpbryQAAAAAA AAAA&ei=H8blS_zcG6S2iwTXo7jZDg&sig2=eZN9G11FxfAhPR03k592jg&gl=us&hl=en&sa=title&ved=0CBIQgwgwAjgA)

D-Link Systems DES-1105 - Tech for Less (http://www.google.com/product_url?q=http://www.techforless.com/cgi-bin/tech4less/DES-1105%3Fmv_pc%3Dgoogle_base%26tts%3D20100508023700&fr=AAYgnPAwlhhGddJ4lFEDNqmM1BzblFsORR7YJT-03lLWYosBkYN1SNmAVdBALneN1SIFm4niHDiG6D2zaDHHzBGmf QlkSixPMSFrfJO0LZkPtovYBG15T_gsy-1rX6FiXY_dIrPRMwvbExkOfDL139RlUbsGbLJEm3jI_bNrVtcc OmGoYpxSU2TrXSBpBx2pOgAAAAAAAAAA&ei=5sblS7PVBJaeiATO-OTYDg&sig2=Mtl8dfmsgl9Rc3uTvnhcZQ&gl=us&hl=en&sa=title&ved=0CBQQgwgwATgA)


You could opt for a little more power by using a Router:
Linksys BEFSR41 Cable/DSL Router - 10/100 Mbps 4-Port (Refurbished) at TigerDirect.com (http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=3537304&sku=L48-2237)