Do you have another scope, I'm guessing all modern scopes use SMPS, and DC-DC converters and linear regulators for all the rails. Find all the power control IC's and regulators/etc, and monitor them on plug in and start-up. They probably have a standby voltage too. Watch them all on start-up, see if any never turn on, or barely turn on, etc. Either because they don't get Vcc, or some signal keeps them disabled, or some problem close by.
IDK these scopes at all, but I'm guessing they have a startup sequence similar to a motherboard or GPU.
, oh I'm a bit late on this thread