Sys admins or Net Techs - Can ya help a fellow tech out?

I work on printers and MFPs. I have a client who cannot ping my MFP when it is set with a Static IP but can when using DHCP. The truth is, the MFP tests good and I am off the hook, but I would prefer to help the client's IT solve the issue. So here is what we have done. Let's assume the STATIC IP is 196.96.16.4 and when we enable DHCP it gets an address of 196.96.2.19. (btw, the MFP has a built in webpage).

Using an ethernet crossover cable, I connect from my laptop to the MFP which is set with the static IP (my laptop is set to an IP one higher or 196.96.16.5 to avoid conflict). I am able to ping and access the webpage. At this point, my MFP tests good and I can go to the next call, but I decide to help the Net techs out.

We reconnect the client's net to the MFP. We cannot ping from the net.

We reset the MFP to enable DHCP. It assigns the address above and the net can ping and access the webpage. Even before the ping, I feel the fact that the server has assigned a DHCP address is sufficient to prove the net works.

Another tech suggest we try to ping the DHCP address again after UNPLUGGING the MFP to insure there is no IP conflict on the network. The logic is, if the DHCP address assigned to the MFP is already present elsewhere on the net, the computer may be pinging THAT device. I find this scenario extremely unlikely for several reasons but it's cheap and easy so we do it. NO ping.

Another tech suggests we set the DHCP address as a STATIC address (same IP address as the dynamic one, but Static). The net now CAN ping and view the webpage.

In summary, STATIC address, no joy. DHCP address pings, DHCP re-entered as Static, pings.

My thought is that the last result is because the server has already established an address for this machine and the server recognizes it, so when we make the DHCP static, it doesn't bother the server. But when we put a DIFFERENT address in as Static, the system won't recognize it.

Ultimately, the customer wants all of these computers set to access the MFP with that STATIC IP. All of the computers recognize the MFP when it is assigned an address through DHCP. But the IT guys don't want to go back and change the driver info on each computer.

Opinions, suggestions, etc.