My 4S keeps restarting and battery life is ridiculous and is acting very strange

So i bought my iPhone 4s in October 2012, so have had it for just over a year but the warranty has run out.

A couple of months ago, just recently after i updated to IOS7 data, i was on my way out and suddenly my phone died even though i had (what it displayed on the screen as) full battery. i charged it the next morning but the whole time i had it plugged in it was restarting every 2-3 minutes.

Since then my battery only lasts a maximum on 6 hours, my phone will die, i'll have to charge it and let it keep restarting itself until it has enough battery for me to leave it for 10 minutes until it stops restarting but has power, to then plug it in and charge it without it restarting. And my battery never displays anything but a constant 3% or 5% even thoough it has full battery.

Now, after roughly 4 months ( i probably should have taken it into apple sooner) my phone dies and it is just flashing the apple logo without even turning on, this starting happening this morning and i don't know what is wrong or how to fix it?

Anyone else had this incredibly frustrating and annoying problem or has a solution to fix it? Any help or suggestions will be greatly appreciated asap!!!!