First, there are no search warrants issued in a civil case. So don't worry about that.
The issue here is what the documents were that you downloaded and what the nature of the business your former employer was in and what your now employer is in. If you were someone that designed something for your former employer such as software or machinery and you downloaded design documents, that could be a problem. But if you were involved in design, then you most likely already had unfettered access to those documents on your company's network and on your laptop. That information would be considered proprietary and belonging to the former employer. But if these documents did not have to do with proprietary property, then I can't see how the former employer would care about the download.
What were the document that they claim you downloaded? And did you share them with any prospective employers?
From some quick searches on the internet, it appears that the proprietary information and inventions agreement act is nothing more than a non-compete agreement. Did you sign such an agreement?