Question Regarding Canon Printer Problem

Hello,
I know you guys usually just talk about the hardware that is in your case, but I just came across a problem with my Canon Printer. The printer stopped printing Black colors from the cartridge. I did a bunch of nozzle cleanings and even a couple deep cleans.
Still things were not right. Now, I just realized that even though the printer was telling me the ink tank was full it was actually empty. I am not real knowledgeable of printers but I took out the cartridge an looked at it.
Since they are clear I was able to see the ink in them. It appears to be completely out but I am not sure if I am looking in the right spot. There is a front compartment and then there is a bigger compartment that looks like a sponge is in there.
Which part of the cartridge do I look at? What would cause the printer to report the amount of ink incorrectly? It is an MP600 that has separate ink colors.
Thanks
