BSOD/crash/reboot at this stage of boot sequence is typically caused by "inaccessible boot device" error which is usually related to missing drivers to access the disk sub system. Often this happens if Windows was installed to an IDE disk (or SATA disk operated in IDE/compatibility) mode and later switching to a mainboard which supports native SATA (AHCI) mode.
There are three solutions for this problem:
- Re-enable AHCI service
- Configure drives to work in IDE mode
- Re-install Windows
To re-enable AHCI it's required to enable the msahci service. If I remember correctly you need to set the start value at HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\msahci to the value of 0 (automatic start). You can do this from WindowsPE if your system is unbootable or by loading the SYSTEM hive located at from %SystemRoot%\system32\config\SYSTEM on any other machine (e.g. by attaching it to an USB-enclosure). However the best method is to do this BEFORE you move the HDD to another machine or before you replace the mainboard.
Alternatively you can try to enter the BIOS of your new machine and configure SATA drives to IDE or compatible/legacy/whatever mode (sorry, the concrete menu item looks different on almost any mainboard). Unfortunately many laptops do not offer such a menu item.
If you managed to boot Windows in IDE compatibility mode you might apply the changes described above to re-enable msahci and then re-enable AHCI mode in BIOS. This would enable AHCI features like NCQ and gains you some HDD performance.
I think it's not necessary to explain the re-install option.
Remember that if you move the HDD to an entirely new machine Windows most likely needs to be re-activated (check system property panel). Also the first boot will likely take pretty long as all devices will be re-enumerated and installed. Watch the device manager for missing drivers.