Answer to "Replaced iPhone4 battery. Now randomly restarts and battery % broken!"When it happened to me I was sure it was the battery or the fact that I changed it. But I did the exact same thing to my wife's iphone and hers worked perfect. So I kept digging and I found out that the soldering broke loose on the battery connection. Exactly where the battery plug connects that connection onto the board was bad for me. They charge $30 more or less on e-bay. Some sellers offer services on iphones and I found one that does specifically the battery connection. I got mine fixed good luck.
Answer to "Replaced iPhone4 battery. Now randomly restarts and battery % broken!"I got a higher capacity battery and had the problem the same as everyone here. I could only see my phone working as long as i was plugged in as soon as i pulled the plug my phone would turn off. Well I plugged it in and went to settings, general, and press reset all. The problem went away and now I have a 2600mA battery instead of the 1400mA original. I also added an external case,battery with an aditional 2000mA I now I don't need to recharge for about two or three days. Hope this helps.