The picture has nothing to do with IR so we need to keep that out of the troubleshooting for now. Cable box was replaced, new one outputs video so video is good.

Its either your cable box is locked up or the IR repeater system has a problem.

What happens when you point the motorola cable box remote directly at the cable box and CHANNEL UP? Does that work? If so you know your cable box is good. If not your cable box is locked up or defective.

The blinking just means that its receiving IR. You could make it blink with a DirecTV remote. An IR repeater system will pass any IR. Im wondering if the new cable box is a different model and the remote you have doesn't control it properly.

Another thing it could be is simple IR interference because of the LCD. You can test this by shutting the TV off. Point the remote at the IR receiver and hit channel up. Go to the cable box and see what channel its on. Then go back to the IR receiver and hit channel up again. Go back and see if its actually changed on the cable box.

If it does change you know your IR repeater system & remote & cable box are good but your TV's light output is interfering with the IR receiver. You can solve this by moving the IR receiver around in the cabinet to see if you can find place that wont get hit with the LCD light but still be able to be hit from where your at when you watch TV.

LCD TV's change over time and the interference can literally show up over night. You may need to upgrade to an RF remote. This will eliminate the IR receiver and the interference issue all together.