Same issue Here.... I fully charged my new 80GB Zune last night before I went to bed, turned it off....
This morning, I tried to turn it on.... DEAD
WTF..... this seems to be a widespread problem.....
Even if the unit was in "standby" or left running for 6 hours, it should not be all the way dead....
It's like the hard drive was running the entire time..... What does MS Tech Support have to say???