I have had this phone (SGH-i777) since November and this problem has started within the last week.
I charge the phone. When the 100% icon appears I disconnect the phone. The 100% icon will not go away.
If I turn the phone off then it shows a battery icon with no fill and a status circle that doesn't turn. After a few seconds it shows a battery icon, partially filled, with 5 white dots beneath the battery icon. Then it shows a black screen. The phone goes back and forth between these three screens. The four white buttons are always lit.
If I take the battery out and put it back in it sometimes starts the battery icon cycle over again and sometimes starts the phone.
If I plug in the charger then the phone stays on the partially filled battery screen, dims, and then turns off. If I leave the battery in and connect the charger I can get the phone to start.
Sometimes when I power off the phone it immediately restarts; the other times it does the battery icon cycle. I cannot turn the phone completely off without removing the battery.
While charging the battery status seems to jump to 100% during the charging cycle but the battery isn't being fully charged.
Let me know if anyone wants to see some screen captures or anything else that might help.