様（よう）がない or 様（よう）もない is an expression used to highlight that there is no ‘method’ or ‘manner’ in which to do (A). It can be interpreted as ‘there is no way to (A)’, or ‘it’s impossible to (A)’.
This phrase will appear attached to the 連用形（れんようけい） (masu-stem) of verbs.

• 車（くるま）も自転車（じてんしゃ）も壊（こわ）れているので買（か）い物（もの）に行（い）きようがない。
  Because my car and my bicycle are broken, there is no way for me to go shopping.
• パソコンが車（くるま）にひかれて粉々（こなごな）になったため直（なお）しようがない。
  It is impossible to fix my computer because it was run over by a car and shattered into many pieces.
• 電話（でんわ）番号（ばんごう）もメールアドレスも分（わ）からないので、連絡（れんらく）のしようがありません。
  I have no way to contact them because I don’t know their phone number nor their email address.

様（よう）がない often focuses on that the action of (A) is not possible, despite that the speaker may actually want to do it.