We recently had some issues where we'd PXE boot an Optiplex GX620 and after booting into WinPE the computer would fail and reboot itself. It turns out even though the computer detects as x64 architecture, it's actually using the x86 boot image in SCCM.
We were missing the NIC driver for that model in that boot image. Apparently Dell dropped it from it's WinPE cabs at some point and we didn't notice it until we cleared the drivers from our boot images and reloaded them (thus losing the original driver support in the boot image).
After checking the motherboard I noticed the chipset was BCM5751. The correct driver on the Broadcom website is the NetXtreme Desktop/Mobile and the Windows 7 driver worked just fine. The drivers that Dell had listed for this model didn't work! After adding the drivers, verify that the boot image has the driver listed by going into Properties and checking the driver tab. Then verify that your DP updated by checking the last update date/time. If not, update it manually and verify. Once that's done you shouldn't have any issues PXE booting your Optiplex GX620's and WinPE should connect to the server just fine.