Chosen Solution
IPOD TOUCH Model A1367 32 GB Unit turns on but does not respond to touch to turn on or off.tried the turn off with awake button and bottom button pressed down .Apple sign comes up and eventually goes off Push awake button ,unit fire up ,same thing happens ,open to unlock sign appears .
Sounds like you having some hardware issues with your screen. I would try a restore through iTunes to double check it is not a software glitch. If same issue, then it woud be a faulty screen and would need to be replaced. Replacement parts and tools can be found on iFixit.