No, courts haven't moved online. Not yet, anyway. You wouldn't be ruling or deliberating on current cases, but you can do jury work from home, and it's mostly for the benefit of legal firms and lawyers. The cases are real, but the names have been changed. Take a look at the website eJury to find out more specific detail and find out how much work they currently have to offer.
Virtual juries are used to help train lawyers, and to give them feedback both before and after trials. You're presented with the evidence in the case, and the argument made by lawyers on both sides, and you return a verdict based on your understanding of the case. Lawyers then use your feedback to develop strategies that will help them when they have to go to court for real. It offers a fixed fee per case, and it's a way to turn your reading time in the evening into cash.