Since it takes GOG about two weeks (and counting) to respond to my support request and there is no other option to reach them (anyone have their email address?) I am seriously wondering if the support system still works. Does anyone else have similar problems? Can someone from GOG's staff comment?

I don't know but if you have a multiplayer game which requires a key on GoG, you can request you multiplayer key. They respond to those mails in 1 or 2 days, so you can test if it works or not.

Let's see a copy of your original support request to see if it was readable and/or understandable, then we may or may not have sympathy for your cause.

Using this means might be more direct and less likely to fail/go into a spam folder.
Always remember to include as much information as possible, including your GOG user name and dxdiag if relevant.

Fine, here goes:
"Dear,
After reading the forums and trying the mouse.ini file posted there, I got my mouse to work, but only partly. The menu never gave any problems. In-game, I have full pitch (Y-axis) control, but only the right half of the yaw (X-axis). So I can only make right turns..
I tried all compatibility modes, but none worked.
Dxdiag file included."
Game in question is Independance War 2, there are more people with mouse problems but I guess theirs are solved by the solutions posted on the forums..
That's exactly the system I'm not sure off..
By the way, I would kind of accept if they would tell me they can't fix this problem and suggest I buy a joystick. Were talking old games without the original support, which are hard enough getting to work on a modern system.
What I don't like is total radio-silence..

I guess they're either sorting out the problem and will get back to you (and others) when they get some answers, or they didn't get your email for all sorts of reasons. Did you send them just one request or a few more when you didn't get a response after a week?

I sent a follow-up after a week, which currently is about a week ago.

If your question went through okay it should be in your account under the My Emails tab. Check that first just to be sure.
Dxdiag includes mouse model, but not driver version (as far as I know). Including that might help them replicate your problem. Remember that this is a very specific problem you're having, as you say that many have resolved such issues already (where they've had any issues at all).
But maybe getting a joystick is the only real solution here, what with it being a space sim and all.
That said, it would be nice if GOG at least sent out some kind of automated message that let you know that they got your message and how long you're likely going to have to wait for a proper response.

I would also include what OS you are using and especially info indicating if it is a desktop / netbook or laptop.
Laptops / netbooks can be a pain due to the special keyboard drivers many use to enable the Fn functions. It can be as easy as turning Num Lock off / on, using only the arrow keys.
I would include as much system info as you can, just knowing if it's a 32 or 64 bit OS or single or dual core can help.

I haven't gotten responses to my support requests either. The first attempt was in April, and just last month, I sent a new one thinking that it might have gotten lost. I too, wonder if something is up. Hopefully, it's just a difficult issue, but it would be nice to have an indication that they received the message.
I hope your issue is solved soon.

He said he included dxdiag, which would cover all of that.

The couple of reports i put through the system got replies in 2-3 working days.
But those were at least 6 months ago, so I don't know if something (technical or staff) is up at the moment.

Well, exactly. I would expect a similar level of service, since I still have the impression of GOG being a well-oiled machine. But how would they find out if their communication system would suddenly malfunction? You wouldn't get a lot of feedback messages about it...

Yup, they're there.

GOG did have a problem with their ticketing system a while back. Some new support requests were automatically being marked as solved (or something like that) which meant no one ever looked at those and they were never replied to. Under normal circumstances, GOG will always respond within 2 - 3 business days, so it does seem really odd that you would have two weeks of silence. I don't think any of us can say for certain what the problem might be, but I would definitely have the broken ticketing system on my list of suspects.