Battery problems

iPhone doesn't show charge more than 1%, however working longer then expecting at this amount of battery charge.

I was playing several games for about 30 min., captured 5 min. video, watched few youtube videos, everything with turned on wi-fi, bluetooth, location services, etc. What logically means nothing wrong with the actual battery capacity, something wrong with the software.

Due to this problem iPhone doesn't turn on, as it probably believe it have low charge, only after several hour plugged to charger (about 4-5) it goes on working again.

Things done:

Hard reset (many, maybe too many times)

Sofware restore

P.S. Before software restore, iPhone was turning on quicker then after restore.

Model: iPhone 4S, 16GB (A1387)

Software version: Latest iOS