I just love going out on a limb! In this case I have no idea what the problem might be, but these are the most fun to try out.
Bring up a command prompt on one of the machines and do an IPCONFIG /all and see what the DHCP server address and Lease Expiration is, and compare those values against expectations.
If you can, try to get a sniffer capture of the attempt as well.
My guess would be that during the IP renumber, some details got skipped, but you’re going to have to provide evidence of this to get the IT department to acknowledge.
It does sound like the client is not getting a DHCP response from the server, or at least some part of the DORA (Discover/Offer/Request/Acknowledgement) process is not getting to either the server or the client. It is possible that the switches have not been properly configured as a “IP Helper” (in cisco terms) to forward the DHCP requests to the server. This is of course assuming there were new switches installed and that the switches (or some of them) were layer 3 switches.