Well, let's see.... I googled "e-machine EL1200-6H"...
The first hit was this thread... the second hit was the product info page on eMachines' website.
Clicked the "Customer Care" link...
Selected "Desktops", "EL-series", "EL-1200"...
Clicked "Driver Downloads"...
Found two listings that included network drivers:
EL1200_CHIPSET_NVIDIA_15.20.zip - NVIDIA Chipset Driver Version 15.20
Supports: Windows Vista (32-bit)
Note: This package contains includes: Ethernet Driver (v67.80) WHQL, Network Management Tools (v67.81) "Sedona", SATAIDE Driver (v10.3.0.33) WHQL, SATARAID Driver (v10.3.0.33) WHQL, RAIDTOOL Application (v10.3.0.33), SMU Driver (v1.45) WHQL, SMBus Driver (v4.64) WHQL, GPU Driver (v175.16) WHQL, Installer (v5.93),
-- and --
EL1200_CHIPSET_NVIDIA_15.15.zip - NVIDIA Chipset Driver Version 15.15
Supports: Windows XP
Note: This package includes the following drivers: Display Driver (v164.01) WHQL, Ethernet Driver (v67.76.1) WHQL, SATAIDE Driver (v10.3.0.21) WHQL, SATARAID Driver (v10.3.0.21) WHQL, RAIDTOOL Application (v10.3.0.21), SMU Driver (v1.45) WHQL, SMBus Driver (v4.64) WHQL, Installer (v5.84)
That second one should be the one you need - again, Windows Server 2003 is built on the XP core, so the XP driver *should* work.