does my iPhone's logic board has problem?

iphone 4 charging problem and doesnt gets detected and update problem(update is looping on apple logo)

okay,so basically this is the problem,couple months ago i dont know what happened but maybe something burnt in my iphone or something else happened but when i charge my iphone and he is turned on he is charging really slow(from 20% to approximately 70-80% over a night) and when he is turned off he charges normally(i have to connect my iphone first and then to turn off so it wont turn back ),my iphone doesnt get detected by any computer too.

and now after couple months i wanted to update to ios 6 from 5.0.1 and it is looping on the apple logo.

so what are my options?