The first two switches that you're showing in your pictures are for AC/GND/DC selection, they're not actuated by the range switch so don"t force them.
Like others said, you should try to gently clean all the leaf contacts by sliding a piece of paper soaked in IPA under them:
Thanks, I did the cleaning with the piece of paper soaked in alcohol, and let the last contacts in peace, after moderate attempts to close the open contact.
Now everything seems to work, but I have also the impression that the fact that the oscillo has been running for a while improved its condition. I will eventually now make a calibration, but I am already quite happy with
the present status of the device.
I have also checked again the ripple by several ways.
Using another oscilloscope (TDS460) and better probes (350 Mhz HP), with basically the same results as with the Rigol.
Using the Keithley 197 to measure the rms voltage in AC mode
(V) nom. ripple measured ripple rms ripple (AC)
p-p p-p (DS1054z) keithley 197
+55 4mV 27 mV 0.27 mV
+15 2mV 20 mV 0.15 mV
+5 2mV 20mV 0.23 mV
-8 2mV 23mV 0.39 mV
+110 20mV 50mV 4.8 mV
Also using the DS1054z with the bandwidth limited to 20 Mhz (I did not find another option). It gives results better than with full bandwidth, but still of the same order of magnitude.
So it seems that I can leave it like that, thinking that the truth my be between the rms voltage and the ripple at full bandwidth.