> I started "repairing" the project but there're no tests to check whether my adjustments are correct. I'm so frustrated and depressed by it.

Even the worst projects tend to have logging. You can hook into that, and whilst it's not great, you can test that correct log messages are made.

The TDD book, does in fact step you through examples with no tests and show you how to hook them in.

It isn't quite as hopeless as you think it is. In fact this is the kind of system I quite enjoy working on.