Chosen Solution
iphone 3gs plugged in takes charge for 30 secs then buzzes and goes ‘buzz buzz’ the apple sign comes on and then the screen goes black and then 2 mins latter the same thing again…..
Sounds to me like your battery is on the fritz ;-) replace that one and re-evaluate. The guide for the repair is here and you can get a new battery from here. Hope this helps, good luck.