Hello and welcome to Apple Discussions.
There could be a couple of causes for the Mac to fail with printing.
1. The printer does not support Postscript. For a number of office printers, the Postscript kit is an option. If you are trying to print to it with a Postscript driver (the Mac driver you downloaded for 10.6) but the device only supports PCL or a Sharp proprietary language, then you will not get any output.
Since there are Windows PCs printing to the copier I suggest you get one of them to do a Windows test print. This will confirm the IP address of the printer and show which printer driver language they are using. As I mentioned, it may be a Sharp proprietary language, which could be a problem as these languages usually only have a driver for Windows - not for Mac.
If they are using PCL then you can open System Preferences > Print & Fax, select the Sharp printer queue and open Options & Supplies. Under the driver tab you can select the print driver. If you change this from what it is currently using to Generic PCL Laser Printer, this will let her print but there is no finishing function (like stapling) but at least it supports duplex (two-sided) printing. Note also that the Generic PCL does not support color, it only prints in b&w.
With regards to the IP protocol, HP Jetdirect-Socket would be the best option. IPP is not always enabled and LPD can require a particular queue name.
2. If the printer does support Postscript then some office printers also have a job control function. This is often used to restrict color printing and when enabled, it can stop the Mac from printing. If the device is a copier and users need to enter and ID/Password to perform color copying then this would indicate it has this function.
You can often check the setup of the printer by entering its IP address into a web browser. This will open its internal web page which shows details about the device, such as the printer languages supported, protocols enabled and if this job control is enabled.
If the device does have some form of job control enabled then there is often a setting within the driver that lets you enter the appropriate details. Sometimes you can see this via the Driver tab mentioned above. If there is no setting there then you can check the driver menus when you select to print.
Anyway, that's about all I can suggest you check. The fact that you can get toner levels indicates that there is a path between the Mac and the printer, so at least you know it is not network related, unless the printer ports are being blocked but I don't think this is likely - especially so if the Windows users are connecting via the same wireless network.
See how you go with this information and reply if you need more help.
Pahu