I had the same exact problem and I was able to fix it! No need to take it to Apple.
(specifically convenient for those of us that got the iphone 3g on ebay)
This is how it happened:
I was talking on the iphone when it said that my battery had less than 10% so, I went ahead and connected it to the wall charger I have for it and continued to talk. 30 mins later the iphone just turned off completely. I was pretty upset to say the least. I went to turn it on again and found the same exact picture being described. I figured I just had to let it be for a few hours on the wall charger.
The next day in the morning I find out that the iphone had the same picture and had not charged 1 bit!
I restarted it (pressed the power and home buttons to force it to shut down and turned it on again) and nothing, same picture. I took out the charger and put it back, nothing, same picture (it would even turn off if I didn't put the charger back in right away).
I then used my USB dock (a dock actually for the old iphone version, but that still works for the 3g, if you force it in). And nothing my computer would not recognize it.
Finally I thought of something:
I placed in the dock and turned it on, once again giving me the annoying battery screen. However, this time I actually restarted my computer. My rational was that if the device was connected while it was booting up the computer had to recognize it somehow.
During my computer's boot sequence the iphone appeared to had turned off, I didn't touch anything though. After windows loaded, I noticed that still the iphone was black as if it was turned off. Thinking that it probably ran out battery once again, I went to turn on the iphone while still having it on the dock (during this whole time I had not removed it from the dock).
And alas! I saw the apple symbol and my springboard showed up!
It is now currently charging (I can see the charge increase on the screen, when I lock the screen, it is now halfway and green) on my usb dock.
I went to place it back on the wall charger though and it seems that it doesn't work. I will be buying a new wall charger soon.
I am thinking when I was talking on the iphone and connected it to the wall it simply never charged and thus the battery completely drained. As soon as I placed it on something that wasn't broken (ie: my iphone usb dock) it started to charge but still was frozen on that (stupid) battery screen. Restarting my computer while connected did something to the iphone so that now it is fully operational. All without having to resort to apple's communist ways of trying to control all aspects of your life.
Personally I'm not an apple fan. I "gave into" the whole iphone thing when I figured out there was a generation of people my age committed into fighting back the apple empire while still using its technology.
Cheers