Cold booting hangs

My Dell Latitude E5530 hangs 19 out of 20 times while power-on booting. When the laptop is still warm it is more worse than when the laptop has been off for some time.

Starting a (warm) reboot from windows never fails

When the booting hangs nothing is displayed and there is no sound, not even a beep. I removed all peripherals.

Also booting into diagnostic mode (battery removed, power button pressed while reconnecting to mains) results mostly in hanging, though immediately the hard disk indicator light starts to blink very regularly about once a second. (so it is probably not indicating reading from the disk)

When booting in diagnostic mode does succeed the full diagnostics run does not reveal any flaws (but then it has booted ;-) )

I have the following questions but any suggestion is welcome

1. Is there hardware module which cause this, and could I replace itWhen myself?
2. Is there a way to diagnose this any further?
3. Is it possible to skip some of the self tests?