Thanks. So you will have to connect the MP620 via USB cable to the Mac and use the Canon IJ Network Tool to get the MP620 connected to your wireless network.
With the printer connected via USB, open Finder and select Applications > Canon Utilities > IJ Network Tool and double click Canon IJ Network Tool. With the application open the MP620 should be in the list, shown as connected via USB. Press the Configuration button then select Wireless LAN. Select Infrastructure for the wireless type and you can then search for your wireless network. Select it when found and press OK. The IP address should be set to acquire automatically and should show what address it has acquired. Make a note of this and then press OK to complete. You should then turn off the printer and unplug the USB cable.
Now you can turn the printer back on and then open Print & Scan to add the printer. At this stage you will probably already have two printers listed, one for the USB connection and the other from your previous restore. Remove them both by selecting and press the minus button under the Printers list. Then click the plus to add the printer and the MP620 should appear with the Default view selected, although it can take a few seconds before it does appear. When it does, select it and press Add. Now you should be able to print. If not, let me know.
Sorry for the delay. This is the point where I'm quite stuck. I downloaded the Canon IJ Network Tool from Canon website, but when I open it I do NOT have the option that you explain here. Instead of seeing the option to connect to Wireless LAN, the dialogue says: "Select the connection method between this computer and the printer." I have the option to "use the printer on the network" or "Do not use the printer on the network." When I tell it to "use the printer on the network," the tool says "Searching for Printers," and then "The pritenr that is connected with the USB cable was not detected. To set up a network connection fo ra new printer, connect the printer to the computer with a USB cable, confirm the following and click OK: The printer driver is installed (check), The printer is turned on (check), the USB cable is connected correctly (check).
If I could get to the dialogue about connecting via Wireless LAN, I think I could fix this thing, but I don't see what the manuals describe I should see in this tool.
Instead of seeing the option to connect to Wireless LAN, the dialogue says: "Select the connection method between this computer and the printer." I have the option to "use the printer on the network" or "Do not use the printer on the network." When I tell it to "use the printer on the network," the tool says "Searching for Printers," and then "The pritenr that is connected with the USB cable was not detected.
You do need to select "Use the printer on the network" and after its search it should show the MP620 connected via USB, as shown below for my MP990.
If you are not seeing the MP620 then that is unusual. Did a printer get created for the USB-connected MP620 in Print & Scan. If you're not sure, remove all MP620's from Print & Scan, disconnect the MP620 USB cable from the Mac and reconnect it. If the cable is okay a printer should be created for this connection. If no printer gets created then maybe the USB cable is faulty. To check, open System Information (Applications > Utilities) and select USB in the left column. The top right pane will show all USB ports on the Mac and if the USB cable is okay, the MP620 should be shown under one of the USB busses. If the MP620 is not appearing then try another USB cable.
Once you have the MP620 showing, you set the top left drop menu to Utilities (as shown in the image above) and then you can press the Configuration button, which will show the network settings for the printer, as shown below.
Once you get the above and an IP address is obtained by the MP620, then you can press OK to exit the tool. The last step is to then turn off the printer, unplug the USB cable, and then turn back on. Now you should be okay to add the networked printer.