computer freezes in safe mode, what now?

After a Christmas period gone sour, I am pretty much out of ideas how to get this laptop (HP pavilion g7, AMD A4-4300M processor) working.
What initially seemed more software or HDD related, now has become a true hardware issue (I guess).

The system does not allow me to re-install Windows 8.1. anymore. It freezes long before it is finished.
I now started in safe mode, was not fast enough to avoid the scan & repair drive and at 69% complete (which took a few minutes) the computer freezes. Is it a fair conclusion that failing at this stage excludes software and drivers?

The HDD is new (Seagate with SSD), I put a win8.1 version on it in another HP g7 laptop. When I put back the HDD in the laptop with issues, windows recognized the different devices and configured itself. (at that time, the computer would finish starting up windows before it freezed).
I have tested the laptop with RAM from another laptop. Different RAM, same freezing issue.
I have vacuum cleaned the outlet of the fan, it was dusty.

So what is next?
(obviously I have done some more things in the past period, but above summarizes where I am at now ...)