Click on this link for a direct download of the Ethernet LAN driver... once download is complete, double click on the .exe file and the installation will begin. Once it finishes you should have internet access via cable. There are several drivers for the same purpose due to different ethernet cards installed on variation of the D620 model. This is the first ethernet driver in the download list so it's the more obvious to download. Even if it's not the exact driver you need, it should connect and help you download the Slim Drivers application so it can install the right driver if it should turn out to be different.
http://ftp.us.dell.com/network/R116105.EXE
For Wireless connection there even more drivers so there is no way to tell which you need untill you can install the hardware information application you can download from the following link:
Install this application to ID devices on the Dell Latitude D620 laptop... that information will help you download the right drivers
http://download.piriform.com/spsetup114.exe
I'm supposing you can download to the computer you're using to post here... so download either the ethernet driver to connect to the internet or the Speccy application to determine which exact ethernet or wireless card you have, to download the exact driver you need, or to give me that information so I can locate the right wireless driver.