My phone was fully charged and docked when the red battery just appeared and would not go away? It's a 4S and a couple of years old, so most likely needs a new battery, which is a simple and inexpensive fix (just google). But I am away in the middle of a vacation, and a huge rain storm from a hurricane, so getting a new batt anytime soon won't work. I tried all the reboot and iTunes fixes, but after six hours on the charger, still a red batt. Then I found this thread about heating the phone to put a slight charge in the batt <http://forums.imore.com/iphone-4s/231912-iphone-won-t-charge-after-battery-drain ed.html>, go to the 16th post by VFRWiz... doing this made my phone alive again, it's all about heating the batt to get it up past the lithium auto-shut down level (which is what the red line battery icon means).
Following is how it worked for me, and my phone is fine now 12 hours later. Do not do this unless you are desperate, it would be best to get a new battery if you can, or into an Apple Store. ALSO be VERY careful not to over-heat the phone, read the entire thread above, as some advise against doing this at all, and there are some other tricks, and finally follow my advice at your own peril:
I used a heat-gun (super-hot & can melt solder, but was very careful not to get too close -most people used a hair dryer) from about 10 to 12 inches away, with the iPhone 4S face down, pointing the heated air at the back right side & edge (where batt is) for one full minute, phone gets pretty hot so be careful, then put the phone back on the charge cord right away. The red battery symbol was immediately replaced with the white apple and a progress bar, then Photos & iTunes launched on my computer and a moment later my iPhone splash screen came up!!! Holy Moly, what a save. NOW THE MOST IMPORTANT STEP: Go get a new battery. Hope this helps someone who is stuck, but do be careful not to overdue the heat, you could damage the phone.
Another post in the middle of page 3 explains the science of the "Heated Battery," which I paste here:
For the Electricians, it's as simple as V / I x R
For the rest of you, Voltage over Current times Resistance.
Basically, heat creates resistance with electronics, and because resistance (ohms) and current (amps) are friends, they increase the value of Voltage.
Example: 30ohms x 5amps = 150volts
If you heat it up, the ohms will rise, example.. 35ohms x 5amps = 175 volts
(note this isn't the actual stats of your battery, just a loose example)
Now because you applied heat to your iPhone battery, or any Lithium Ion battery with a circuit that cuts off when it drains too low, you re-enable the circuit because you charged the battery slightly through raising the resistance inside of itself, thus rising the voltage. (very neat trick, eh?)
Another thing about this funny science thing is... if you are a person who wears a wrist watch.. have you ever wondered why the battery in your watch lasts so much longer while you are actually wearing it all the time?