You have said that both you computers are running Windows 7, but you haven't said if they are both 32 or 64 bit versions.
What type of printer is it, manufacturer, model name, model number?
Does the manufacturer have a windows 7 driver for this printer for your version of Windows 7?
Try this method and see if it works for you
Open Devices and Printers
Select add printer near the top menu bar
Select add local printer
Choose Create a new port and local port from drop down arrow Click Next
In the enter a port name do one of the following
1.
\\MachineNameHostingPrinter\Printer'sShareName or
2.
\\ipaddressOfMachineHostingPrinter\Printer'sShareName
In the install printer driver dialog box do one of the following
1. In the left panel select you printer manufacturer and in the right panel select your printer model (to use Win7 native drivers) or
2. Select the have disk button and direct the install process to the folder where you have download and extracted the Win 7 drivers for your printer.