Inspect your printer for an internal print server. In order for a single printer to handle print requests from multiple computers, a print server is required to coordinate priority and keep the requester's identity associated with the particular print request.
Obtain the MAC address of the print server for the dell printer that you will be adding to the network. The MAC address is a unique address that identifies each computer on the network. The MAC is the hardware address of the printer.
Open the router configuration page and enter the MAC address of the printer in the network. Once there, update the hardware addresses in the router configuration utility. Save the configuration and reset the router by unplugging it from the power plug. Dell provides a piece of software called the DEll printer network printing wizard. Connect the network hardware together properly, run the network printing wizard and follow its instructions for any other steps required to ensure reliable network printing on the new printer from each of the users on the network.
What router brand do you have ? Linksys, Netgear, etc.... ?