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The Error 311 indicates a communication error between the Mac and the printer. If you upgraded the Mac from Leopard to Snow Leopard, there could be older driver files for the iP4300 that are conflicting with the new driver. Therefore I would start your repair by trashing all of the Canon files.
The first step is to disconnect the USB cable between the printer and the Mac.
The next step is to delete the current printer queue for the iP4300. Open Print & Fax, select the iP4300 in the list and click the minus ( - ) button to remove the queue. You can now exit Print & Fax.
The third step is to remove the Canon files. These are located in HD > Library > Printer > Canon > BJPrinter. Select all the files inside this folder and trash them. Then empty the Trash and restart the Mac.
With the Mac restarted, you can now run the installer for the 10.6 driver you downloaded from the Canon web site. Ensure this driver is version 10.26.0.0.
Once the driver has been installed you can connect the iP4300 USB cable to the Mac again and open Print & Fax. If the install has worked, the printer should automatically appear in the Printers list (note that this can take several seconds). If the printer does not appear, click + to add and select the Default view. The iP4300 should appear in this view. Select it and click Add. You may get a prompt stating the printer is already installed. If so, cancel this install and try printing with the new iP4300 queue.
If the error message still occurs, then I would try another USB cable. They have been known to cause the 311 error.
Pahu