1. Thank you all for your replies. I contacted Hameg and they sent me the service manual which is not so extended as the one that blacknoise posted above (Thx blacknoise). Apart from that, they've also sent me the first revision of HM604 which I upload here
http://ul.to/geithi8e,
http://ul.to/a94cmlub, in case somebody else needs it.
2. I noticed that when I tapped the left Volts/div switch, the input signal gets distorted. So before tackling the calibration process, I believe it's the right time to give a nice clean to the contacts.
Here are some photos of channel 1. Needless to say that reaching this guy was a pain in the a**.
The contacts were cleaned with a generous load of IPA.
Bits and pieces waiting to be fitted back on the front panel.
Cheers.