Hello, not sure if this would help, but this is what I would try to do:
1. Take the machine off the network, and let it fall asleep. Once it falls asleep try to use the touch screen to wake it up. If it does, then there might be an issue with the formatter board.
2. I would try connecting to a laptop directly, off the network, try running test prints. Then, let it fall asleep, at this point send a job to it to see if it wakes up. If it does, then it would lead me to believe something on the network is causing it to have issues, as you stated, you replaced it with another like model and the same thing started happening.
One last thing, is there any error codes on the event log that coincide with the issue?
Hope this helps.....