Your post doesn't make sense to me. A DHCP server will provide addresses for any computer that requests it. Its IP address does not need to known, since the bootp request is a broadcast message (sent to 255.255.255.255).
You should be able to tell which DHCP server supplied the address based on the scope that the IP address that gets assigned to your PC falls into.
As far as an ipconfig "like" utility, I think that the closest you will get is the net command. Try "net config" and see if you can locate the information that you are looking for.
Ultimately it will probably be easier to put another machine alongside the DOS box and sniff the bootp requests and responses using Wireshark or tcpdump.
pansophic