方法 and 手段: methods and means
Compare how something is done with the means used to achieve a purpose.
How to do something
方法 (ほうほう) means a way or procedure for doing something. 「使う方法を教えてください」 asks how to use something; it does not report having tried it.
「別の方法を試しました」 means trying another method. It does not specify success, so do not add that the problem was solved.
A means toward a goal
手段 (しゅだん) means a means of achieving a purpose. 「移動の手段を考えています」 says that the speaker is considering means of transportation, without having specified a choice.
「交通手段は電車です」 identifies the train as the means of transportation. It states what is used rather than how to buy a ticket.
Contexts of overlap
Both 「連絡の方法」 and 「連絡の手段」 can refer to ways of contacting someone. 方法 may focus on the procedure and 手段 on the means toward a goal, but the distinction is not absolute.
「方法を変えても、目的は同じです」 says that the purpose remains the same even if the method changes. A change of means is not necessarily a change of goal.
Does 「方法が分かりません」 mean there is no willingness to act?
Show the answer and why
No. It means not knowing how. Willingness is not specified.