I have found that sometimes the BJC 600 series gets confused and needs to be reinitialized. If you haven't already done so, unplug it from the wall, wait 60 seconds for the internal supply capacitors to completely discharge, then plug it back in and try again. When you remove it from the AC line it goes through a complete warm up cycle and resets itself.
Also, the contacts that mate with the print head are notorious for oxidizing. You might want to carefully clean them (lightly) with a pencil eraser and some isopropyl.
If these remedies don't work, the Canon 1-800 number will put you in touch with their tech department, and they are really quite good at determining what the problem is over the phone.
(From: Al Savage (firstname.lastname@example.org).)
When I was working on printers, we'd see a few of the 600s in with corrosion on the ribbon cable end under the printhead. NewKote apparently had a venting problem with their copykat ink cartridges, where in some situations ink would spurt (leak? drip?) and somehow corrode the ribbon cable.
I never tried to replace one and see if it could actually be repaired with just the cable, but I did try vigorously cleaning the cable end: no conclusive repair.