I need a Driver for my Dell Demension 4600 to enable my ethernet controller.

It should be available on the dell website, you may have to look it up by model and serial number and know what operating system you use.

see if this is the right driver-

<a rel='nofollow' href="http://support.dell.com/support/downloads/download.aspx?c=us&cs=19&l=en&s=dhs&releaseid=R64645&SystemID=DIM_P4_4600C&servicetag=&os=WW1&osl=en&deviceid=3597&devlib=0&typecnt=0&vercnt=2&catid=5&impid=-1&formatcnt=0&libid=5&typeid=-1&dateid=-1&formatid=-1&source=-1&fileid=84196">clicky</a>

http://support.dell.com/support/downloads/download.aspx?c=us&cs=19&l=en&s=dhs&releaseid=R64645&SystemID=DIM_P4_4600C&servicetag=&os=WW1&osl=en&deviceid=3597&devlib=0&typecnt=0&vercnt=2&catid=5&impid=-1&formatcnt=0&libid=5&typeid=-1&dateid=-1&formatid=-1&source=-1&fileid=84196