Well, printers are either local (attached to a computer via USB, infrared or parallel cable - haven't seen the latter quite some time :) or networked. Networked printers have ethernet or WiFi adapter in them.
Unless printing for you is prohibited on that network (there are several typical ways how to restrict it), if you can reach the printer via network (ping), you should be able to print on it. Provided that the driver is installed on your computer and there is nothing that restricts communication between network segments.
So the IP on different segments should have nothing to do with the printing problem.
Of course, there could be some different scenarios depending on the printer model and how the network segments are connected. Firstly if there is a firewall router in between, it could be set up to pass through ICMP (ping) but to restrict some or most ports. This is doubtful as your printer is "seen" and that does not happen through ping. Also some printers might use more then one port for connection so possibly can see, but cannot print. To be sure it has nothing to do with your network, you could bring it to your segment and connect to your PC from there (I suppose you will need to change IP address of the printer then). When you do that you would need to disable local firewall on you PC to be sure that traffic to/from your printer is not restricted by that.
If it is not network fault, then you need to seek more specific information about your printer and troubleshoot from there. Chances are - if another computer can print to this one, you will be able too.