Since you have a new router with a new encryption key, you will need to configure this information into the MP620. To do this, you will have to connect the printer to the Mac via USB. While this will automatically create a USB print queue, which you will not be able to use once the printer is configured and connected back to the wireless network, this queue will allow you to manually change the network settings in the MP620.
With the MP620 connected via USB, open the Canon IJ Network Tool. This is located in HD > Library > Printers > Canon > BJPrinter > Utilities. With the tools menu set to Utilities, the MP620 should appear in the list of available printers. Select it and press Configuration. This will open another window where you can set the Network Name (SSID) and the Encryption method. The Configuration button as this window will allow you to modify the password (key). With the correct details entered, OK the settings so that they will be saved to the printer.
Once this has completed, you can turn off the printer, disconnect the USB cable and then turn the printer back on. Allow a minute for the printer to connect to your wireless network and then open Print & Fax to add the network printer queue. Depending on which driver you have installed you can add the printer by clicking Default and waiting for the Canon MP620 to appear (with canonijnetwork shown in the Kind column) or you can open More Printers > Canon IJ Network. The MP620 should appear in this view and after selecting the Print Using menu will automatically select the correct driver.
Hope this gets you going again.
Pahu