Adding computer to home network?!?

[Pocket Full Of Sunshine]

I am trying to add a new computer to my home network, but first time doing it and finding it really confusing. It said I needed an adapter (2Wire PC Port Phoneline Network Adapter HPNA) similar to this one--

http://cgi.ebay.com/2Wire-PC-Port-USB-2-0-Phoneline-Network-Adapter-HPNA_W0QQitemZ300212018997QQihZ020QQcategoryZ67869 QQssPageNameZWDVWQQrdZ1QQcmdZViewItem--

but instead I bought a TRENDnet USB to 10/100Mbps Fast Ethernet Adapter --

http://ecatalog.flashecom.com/espec/Thumbnail/10186547.jpg--

because I figured it would be the same thing. I put the software in drive, but nothing seemed to be installed. I carried on with the installation of DSL on the new computer, but then it said that there was no connection with my 2Wire machine thing, which I thought only needed to be connected to my original computer. Did I connect something wrong, or did the adapter I bought is what's wrong? I'm really confused. Sorry if this is really long.
original computer--Dell
new computer--HP
2Wire modem
wired (phoneline)
connected adapter then did dsl installation on new computer--
all this was needed to be done according to instructional dvd