Looks like the Ethernet listed here:
http://ftp.dell.com/published/Pages/optiplex-3020-desktop.html

PCI VEN 10EC  DEV 8168 SUBSYS 0612

RTL8151GD LOM Driver PCI Express Gigabit Ethernet controller

http://www.dell.com/support/drivers/us/en/19/driverdetails?driverid=9V44D

Systems

Operating Systems

MS Windows 7 32-bit

MS Windows 7 64-bit

MS Windows 8 32-bit

MS Windows 8 64-bit

Yes, that lists the drivers available for the 3020. My problem is that none of those drivers match the error I'm getting:

A connection to the deployment share (\name\DeploymentShare$) could not be made. The following networking device did not have a driver installed.

PCI\VEN_10EC&DEV_8168&SUBSYS_06121028&REV0C

I've gone though and looked at the details for every Realtek driver I've downloaded, and they don't match. Some come close with SUBSYS_0611... and SUBSYS_0614.. but NONE have SUBSYS_0612...

Firstly, only the first download link on that page works; the second brings me to the support home page (which I've already visited numerous times -- I've downloaded all net drivers that come up with my service tag). 

Do me a favor: download the file from the first link on the page you referenced, extract it and follow the trail 9V44D > Win 7 > NDIS6 > x64. Open rt64win7.inf in your favorite text editor and CTRL + F for "SUBSYS_0612" and let me know what you see.

Not to be rude -- I appreciate any help -- but you're just pointing me to stuff I've already done. I've downloaded the drivers from Realtek. I've downloaded the drivers from Dell. If I'm not looking in the right place for the driver in the downloads, please let me know. 

I downloaded the file in your first link; extracted, Windows > WIN 7 > NDIS6 > x64 and it's exactly the same as my previous post. CTRL + F "SUBSYS_0612" Not found.

Ah! That would explain why I couldn't find 0612 anywhere. So, theoretically, since I'm trying to use Win7 x64, I should only need http://en.community.dell.com/techcenter/enterprise-client/w/wiki/5084.optiplex-3020-windows-7-driver-cab.aspx is that correct?

I really appreciate the help!

??? this is a network card issue. 

Your other post is just pointing me to stuff I've already done (not trying to be rude -- I appreciate any help). I've downloaded the drivers from Realtek. I've downloaded the drivers from Dell. If I'm not looking in the right place for the driver in the downloads, please let me know. 

I downloaded the file in your first link; extracted, Windows > WIN 7 > NDIS6 > x64 and it's exactly the same as my previous post. CTRL + F "SUBSYS_0612" Not found.

 PCI devices do not enumerate correctly if CHIPSET drivers are not installed first.  The Driver Cab Collections have ALL the drivers. The  RTL8151GD  and Realtek ALC3220 HD Audio Codec are the only Realtek components.

http://downloads.dell.com/FOLDER01766317M/1/3020-win7-A00-P9T2J.html

Realtek ALC3220 High-Definition Audio Codec