Hello! thanks for your answer.
Well when I say the camera seems to work well I mean in term of it's mechanism. No elements seem to be damaged etc. But of course I am not 100% sure. Yes I read the manual, the batteries are inserted correctly. The manual said the batteries need to be cold, so yesterday I put them for a while outside and then in the camera again, I turned to check and the light when red once, I tried to see if it worked, I shot twice and then the mirror got blocked.
How can I know if the compartment is clean? Is there a way to clean it?
The mirror staying up is consistent with a bad battery (batteries are not the only thing that could be the cause, but the most common).
First, I don't remember every seeing in the manual that batteries should be cold. If they are very cold, their output is reduced. So try them again at room temp.
Second, I realize your original post said they were SR44 silver oxide, but are they actually marked SR44? Sometimes a dealer will not be aware of the difference.
Third, the spring contact at the bottom should be bright and shiny. If not, and you see green residue, wide it off as best you can with vinegar on a cotton swab. An ink eraser works as does a bit of emery cloth glued to a pencil eraser. Or fold the very end of an emory board so it can be held against the spring and rotated. Make sure the underside of the battery cover is clean too.
Finally, you might try lifting up gently on the spring contact if it appears flat against the bottom of the battery compartment. Not too much though.