I had a post on this a month back, same issue. I consider it a flaw in the camera but other's don't. I've found that your flash batteries are most likely dead, the flash will still go off, but something about not having fully charged batteries causes the flash to tell the camera when it's focusing and locking "do not use the flash" I've had my camera go all the way to 2" exposure with the flash on. I call this a defect that the camara will go so far under acceptable shutter speed to compensate for ambiant light, even if there is a flash attached. There should be some way to lock or set a preference. for some reason Canon has coded the firmware to do it's best to go for 1/60 shutter speed, even in there's enought light to go 1/250 wiht perfect exposure, the camera will always go for the slowest shutter speed it can. This causes your shaky hands icon and blurry pictures. I would code a camera to always use the highest shutter speed possible to avoid blur, but I'm no expert, just going off common sense.
IMO Somewhere between the G6 and 420EX there's a bug.
From my experience your issue is the flash batteries. then if that still doesn't work, your in the same boat as me with a bad camera firmware. No fix at this time.