I was born into a poor family, so my parents didn't have money to send me to university.
この場合、次のような言い方ができますよ。
ーI was born poor, so I couldn't go to school.
「生まれながらの貧乏だったので、学校に行けなかった」
ーI was born into a poor family, so my parents didn't have money to send me to university.
「生まれながらの貧乏だったので、両親は私を大学に行かすことができなかった」
「生まれながらの貧乏」は to be born poor や to be born into a poor family のような言い方ができますよ。
ご参考まで!