So after going at like 10-12 repair shops (don't remember actually as I lost all my weekend on it) nobody wants to open and clean my N900.
They all give the same response : it is an old phone and it doesn't worth the effort from them to deal with it cause they will have to do some research and stuff.... they are just a bunch of lazy.

So, what I will do : first buy a second N900 (as this one was my main and only phone, got to replace it with an old nokia phone for now), then get the necessary tools (will have to look for what I need exactly) and open it myself. I never had to deal with opening a phone (not even a laptop) until now, but like they say "you have to start some day".

Thanks t-b for the link it will certainly help me.
Also, I will have to recover my backup from backupmenu on the n900 I will buy next week (if I find one worth buying), but I've seen on the forum that it is discouraged to recover a backup on another device (but I don't remember why).
I hope it is doable as that was the intend of the backups I did, to use them on another n900 when the one I have will fail.