I don't have any specific experience with the 8139, but from your description the DHCP failure message from the DOS client has to mean that there is some kind of problem with the DOS network drivers. Trying to obtain an IP address is the first thing the TCP stack does, so if there is a major problem with the network drivers, that's the error you will see.
What isn't so easy to tell is why they fail - all the Ghost applications can see is that they got no response to their DHCP request. The source of the problem could be in several places, and it's tricky to say exactly why.
For instance, it appears that there at least 4 different revisions of the 8139 chipset in circulation (and some "compatible" variant designs from other manufacturers), so it may be that the auto-selection hasn't found quite the right driver. It may pay to have a close look at whether there are any other network templates you can try (I just took a look in GSS2, and there are templates for both "8139" and "8139c").