I have had nearly the identical experience.
The camera was outstanding for 14 months, then the lcd screen went fuzzy and the camera turned itself off.
After playing with the batteries, I can get some response though if I try to take a photo I get the E16 error and a black screen.
The response of the camera changes drastically when I wipe or manipulate the cover for the batteries, which is interesting.
The problem seems to be directly related to the batteries. If I use regular AA's, they die within minutes, though the initial camera response is better with a new battery.
Canon wants me to return the camera but it is not on warranty and I want an explanation from them first as to why there are so many reports of this issue.
There is clearly a flaw with the camera.
There has been some written about this, but nothing definative as yet. The problem is called a "communications error" by Canon, which is codespeak for "We don't know what's wrong, send us the camera and we'll fix it for 100 bucks not what it's out of warranty."
The problem: I turn the camera on, the shutter opens, the lens extends, there is an audible click, and the lens closes and the camera shuts off. Simultaneously, on the monitor the screen comes up, though a bit dark, illuminates the picture, there is some pixilation and lines at the bottom of the screen, and then goes black as the camera turns off, save for a white E16 code in the lower left corner of the screen. This all happens in a matter of seconds, on all settings EXCEPT the digital film setting, which shoots and records fine, without a hitch. I can turn the camera on on that setting with no problem, but all other settings cause the aforementioned. All the review features on the camera work fine too.
The Canon guy told me to change the batteries, reset to factory defaults, remove the memory card, which I did to no avail. He also told me to change the date/calendar battery, which--when I asked him where it was housed--he came back five minutes later to say that my model doesn't have one. Instores confidence, doesn't it?
The maddening things are: a) the camera is 1.5 years old, just out of warranty, b) has been taken very good care of on my end, c) takes fabulous pictures, and d) did this E16 shut down thing for a week, was fine for a week, but now is doing it again this week.