What's the firmware version that you have installed? There is an update firmware for this printer "1600n_NS_EFS.EXE". This has solved a few scanning problems on the network.
Printers: Dell 1600n Multifunction Laser, Patch/Upgrade, Windows 2000, Windows XP, English, French, Spanish, Multi System, v.(1600n SW V1.24 and FW v1.22), A02
Try this if you haven't done that, this should solve it.