Did you plug your laptop cable into the same port as your desktop? If not, you may have to get someone to configure the switch port to be on the same VLAN as the desktop.
If so, then using the same setup as your desktop (with a different, unused ip address) should work. This includes DNS.
If you are not seeing the printer, then this may be that your VLAN/network is different to the printer's, and your network is not configured to forward the broadcast/multicast needed to find the print server.
Either way, is there an administrator for your Local Area Network? He/she should know the network topology.
Regards.