Speculating you have the standard broadcom gigabit ethernet port you can try downloading and installing the following driver file to the D620. Presuming you can't download to the D620 download to a good computer, then copy the file over with a flash drive or CD and install the file.
Another thing to check is in Device Manager, expand the Network section. Is your device listed there and is anything yellow-flagged?
<ADMIN NOTE: Broken link has been removed / replaced from this post by Dell>