Hmmm ... running Memtest86 5.01 as installed by the Zorin installation procedure on the HD shows only 3327 MB- a little bit more than Linux, but not the full 4096 MB installed.
Running AND OBSERVING the BIOS RAM test shows 4096 MB, BUT after 33xy MB it just jumps to 4096 instead of displaying all the numbers in between.
The problem is not the RAM itself - that worked well on another system for years.
But it seems that "something" on the Motherboard prevents PAE from happening, despite CPU - and presumably also the Intel chip set - having the relevant capability. Maybe HP just wanted to save a few pennies on the extra address lines on the motherboard.
(There is no BIOS option in sight to "switch on" PAE.)
The BIOS "system information" just adds up the SPD size values from the RAM sticks - and brazenly informs the user about 4096 - or 6144 - MB "installed memory".
Very clever, HP DC7600 BIOS!
And even litigation proof, as every IT lawyer will be happy to explain, that INSTALLED memory is not the same as USABLE memory.
...
Well, as often in such cases, I COULD have found this out myself, had I not been blinded by my rash - and unspoken - assumptions.
So all that is left to me is to THANK YOU VERY MUCH for your well chosen hints which finally guided me to the solution.
...
And meanwhile I even found the fine print in the HP DC7600 manual, stating:
"Above 3-GB, all memory may not be available due to system resource requirements."
How true...