When you're in a bad way, you're having a really hard time. You might be in a bad way because of money problems, or because you've lost your job — in any case, you're probably feeling unlucky.
Someone who's in a bad way is struggling, perhaps trying to figure out how to pay the rent or how to get a broken down car running again. You can use the expression in a bad way to describe an inanimate object — like a dilapidated barn or a failing school — but it's most common to talk about a person, whether she's sick or troubled or broke, as being in a bad way.