结构剖析
让步状语：Although parents believe that having the internet at home is important to their children's success in school,其中——
嵌套主句：parents believe that——父母们认为
嵌套宾语从句：having the internet at home is important to their children's success in school,
宾语从句中——
--主语：having the internet at home——在家上网这件事（动名词短语）
--谓语部分：is important to their children's success in school——对他们子女的在校成绩来说很重要 （系动词 + 表语 + 状语）
主句——evidence linking access to success is lacking 其中——
主语：evidence linking access to success——链接通向成功的证据（核心词evidence + 分词后置定语linking access to success）
谓语：is lacking——是不足的（系表结构）
翻译：父母们认为在家上网对他们子女的在校成绩来说很重要,但是链接通向成功的证据是不足的.