It appears to be the IR repeater system. We know the remote is good and the cable box is good because they work when you avoid the IR repeater system.

We know that the IR repeater system still does not work when the TV is off so that rules out the LCD.

Even though the repeater system is flashing i think it needs to be replaced.

An RF remote would communicate wirelessly with a 'base station' that you would locate near the cable box that then sends IR down an emitter to the cable box. It basically replaces the IR receiver with a wireless RF signal.

I dont know if you need the RF remote though. My guess is a new repeater will solve your problem and give you the exact same functionality you had before this started. Either option will typically cost the same.

You mentioned changing the power supply. Did you verify the power output was the same as the old one? It may not be powerful enough or may be to powerful to function properly. The original power supply failure may be a sign of internal failure to the connection hub meaning a new power supply wont fix it.