Very interesting. About one week ago - for absolutely no reason (unit was working fine for 5 months and I did nto change anything) I started getting exactly same behaviour. It would turn off after 5 seconds even without any cables attached, just the power.
After spending an hour on the phone with various levels of tech support, I got RMA

They did not seem to be familiar with this problem. Some kind of time bomb bug in firmware? I was running 1.08.