OK, got it to work!
"Usually", electricians wire the hot wire on the bottom to a switch or outlet. On this unit it is "backwards". The RED wire is the Load (to lights) on the bottom and the BLACk is the Line (HOT) on the top. Even though I noted this design issue, I inadvertently wired it backwards after having put in probably 6 of these in friends' homes! Worked like a charm as well as put in a second one in about 5 mins.
I asked tech support why this would happen, but he said to check the fuse and neutral wires as he was focusing on no backlight, I, of course, told him I had wired it correctly! But, he should've known immediately that:the reason for ALL these symptoms is that there is no power to the unit, and that the Hot/Load wires are switched!.
1. The backlight doesn't come on; (because backlight works on 120V, not on battery, so no power to the unit)
2..The LCD goes off in 10 seconds (It is running in battery save mode, so probably no power to the unit)
3. The switch doesn't control the lights, even though the timer is set correctly, and the timer is working (Lights work on 120V, so no power to the unit)
4. You cannot turn the lights on manually (Lights work on 120V, so no power to the unit, this is definite give away, if it is manually not responding)
5. Panel fuse is working as the other lights in the same gang box are working (120V power is coming in correctly).
The incorrect wiring was my fault, but Leviton tech support ought to read this, so they have a map to troubleshooting this particular problem. Hopefully, others will read and benefit.