tinker - Attempt to repair or improve something in a casual or desultory way, often to no useful effect

Mitch tried to tinker with his computer before realizing that it was more broken that he had thought, and that he had to bring it to the computer store to have a professional repair it.
badger - To repeatedly and annoyingly ask someone to do something.
Every time that Arnold asked Samantha to go out on a date, she would tell him firmly ‘No’. But each time he saw her, he would badger her again and again about wanting to go out, and again she said 'No!'