Madd_Mann's method did not work in my case (a batch of 3 EN Deskpro's), but he gave me a clue. Thank you M_M!
This is how I did it, and how, at the end, I understood why M_M's method did not work for me.
First: verify in your BIOS that the cover is unlocked. If it isn't, do unlock it.
Then REBOOT! (Why? => the hardware lock is only unlocked at reboot. You can hear the unlocking 'click'.)
Shut off your PC and disconnect the power cable.
Press the 'thumbholes' at the two sides of the cover.
Prevent the 'ears' from jumping back by inserting two small pieces of folded paper of wood into the slots you created just before by pressing the two 'ears'.
Position a small wooden block on the rear side of de PC on the upper edge of the cover.
With a small wooden, rubber or metal hammer GENTLY knock on the piece of wood resp. the rear upper side of the cover.
The cover will then shift about 1-2 cm to the front of the PC and you can easily lift it off. (Note: your PC will not feel anything of your knocks, because it just stays where it is.)
Do your things, but also clean the sliding surfaces of the cover and the PC-frame. It really makes a difference!
Once the sliding surfaces are clean, you can do it 'the Compaq way'. Just press the thumbholes, slide the cover frontward, and at the same time, move your fingers from the 'thumbholes' to the front part of the ears. It is as if you fingers are sliding over a bump - which is what Compaq actually want you to do. This is the easy way.
If method #2 doesn't work, press the thumbholes and try to shift the cover frontward. The actual shift may be less than a mm, but this is enough for the ears to remain in the 'open' position. Then, with one hand / your fingers / your nails slide the upper rear side of the cover frontward, whilst with another hand, pushing the lower part of the PC (the grey band with 'Deskpro EN' on it) backward. The cover will now slide frontward.
The 'sliding-over-a-bump'-movement in method #2 explains why M_M's method did not work. By pressing the thumbholes, you are locking the cover!
If you study the inner side of the cover you will not see any thing that may retain the cover when it is locked. It is interesting to see how the Compaq designers arranged it.