SSD in old notebook - "No bootable device" error

[salamara]

I want to upgrade my parents' old notebook with a SSD to make it less slow (currently the HDD seems to be the major bottle neck).

I cloned the HDD to the SSD (same size) using  the EaseUs Todo Backup Free 13.0 tool, then replaced the HDD with the SSD. When booting I get the "No bootable device -- insert boot disk and press any key". I have repeated the cloning process a number of times and it always succeeds/finishes, but the result when booting does not change. Twice, out of a number of attempts (20?), it has actually booted successfully and I have been able to run it for a while, but when I tried to reboot it fails in the same way again.

This makes me think that the cloning of the original HDD has actually succeeded, but the SSD is just not (in most cases) detectable by the notebook. Also, it does not seem to be a temporary start-up issue, since the SSD disk continues to be undetectable after the inital part of booting (e.g. when attempting to do a "Primary Hard Disk Self Test" in BIOS the result is "Hard Disk Not Exist" and it is also not shown in GParted when booting from a live Ubuntu USB).

If I connect the SSD via the USB-to-SATA adapter all the expected partitions (copies of the HDD partitions) show up, and they are also marked as healthy when running "list volume" in Power shell -> diskpart, so it seems to be OK in some sense...

Could it be that this SSD is not compatible with the notebook at hand? If so, does anyone know a compatible SSD (is there a list)? 

From the specs i noted that the original HDD (Hitachi  7K500-500, HTS725050A9A364) has a power rating of 5V/800mA DC compared to 5V/1.2A of the SSD. Could it be that there is just not enough supply current for the SSD?

I seem to be stuck, so any help is appreciated.

Notebook product number: XC687EA#UUW (model G62-a36SO)

SSD: 860 EVO 500GB, Model MZ-76E500