The front panel lights of Ref, Math & Digital glow sequentially and stops there.
It looks like, the boot process stops at this point. Thus it would be better to change the title of the thread to "DSO-X 4154A no boot"
It would be helpful to see the output at the UART to get an idea at what exact point the boot stops as this might lead to the cause.
My DSOX4024A (from January 2013) also recently started to stop booting every 2nd day and it then needs another try, sometimes 2x (off-on) is not enough and it takes several times. Firmware is the latest version. Thus this service note 3 would be of interest for me too. I am wondering if the flash problem also occurs at (maybe only earlier) DSOX4000 series scopes? Maybe Daniel can help?
Edit: I also found the thread, where this service note (MSOX4154A-03) was mentioned:
https://community.keysight.com/thread/35583Google finds nothing.
Does anybody have an idea?
Edit2: Did you check the voltage of the battery on the board (visible on the bottom of the first of your pictures)?
Edit3: While this is the correct section repair, you would get much more and qualified answers if you would ask this question in the section
test equipment. There are many Agilent/Keysight hanging around - and they probably do not look often into the repair section.