What is the Difference Between 方法 and 办法?
I don't think you guys are completely understanding it, there is a philosophical difference in the two words. It's possible to 有方法但是没办法. 方法 refers to the general method or way something can be done. 方 means prescribed, 法 here can be understood as way. 

So 方法 is the general or prescribed way something is done that humanity has discovered. 办 means doing，法 here also means way. 办法 refers to someone specific actually doing it. For example:

我的病其实治疗方法很简单，就是每天跑步。但是没办法，因为城市太拥挤所以没有地方跑。Here, I know the way to cure my illness, but I can't specifically carry it out due to individual circumstances.