I've gotten in touch with Canon and have something a little different to try. At the very least the error should change. (Sorry, gallows humor). Please read this entire response before taking action.
After the upcoming test procedure, I have included a link and procedure to contact Canon tech support. The assure me they will replace any faulty tanks.
The purpose of this exercise is either rule out ink tanks that are behaving or isolate the one(s) responsible for the 1414. You should write down the results of this test. Please perform the following:
1. Open the printer and remove all ink tanks.
2. Insert a single ink tank in the printer then close the cover.
3. Confirm whether the printer recognizes the installed tank properly. If it does, it will indicate it does not detect the other ink tanks, as they are not currently installed in the printer.
4. Repeat steps 1-3 with another ink tank.
5. If the printer at any time indicates two of the same ink tanks are installed, the cause will be the last tank installed. For example, if you inserted an ink tank earlier, and you later inserted another ink tank, and it said two of the same inks were installed, the cause of the issue is the last ink tank. Click here
for the Canon PIXMA iP4200 support page
Then click on e-mail support.
Fill out the form.
Under description, supply the following info:
Error 1414 Ink tank problem on my Canon PIXMA iP4200
The error won't go away.
I have replaced the <color in question> tank, reseated it, yet the error remains.
You will also need to list what inks are being used in the printer. State the type of ink that is being used and the order that the tanks are installed in the print head.
Provide the exact part number (such as BCI-6C, BCI3eBk, etc.) if possible.
The Canon support rep assured me they will be glad to replace the malfunctioning tank(s) for you at no cost. Please
respond with the results, and specify the ink tank(s) that were not recognized correctly.
They responded quickly, professionally and apologetically. They want to help get this resolved for you.
I hope this helps end the frustration you must be feeling. If you need additional help or clarification, click the ASK button.
If you could take a moment and rate this response, I would appreciate it.