I bought No Man's Sky the other day, I played to the game without any problem, but today when I want to play it, the game start to update (from version 1.30 to 1.31) but it doesn't start, and automatically it tries it one time and another but nothing happen. I try doing the "verify/repair" option and then I receive a message saying "Failed installation: problem accessing the disk", then I uninstall the game and tried to install it again and I receive the same message (so now I cannot even install my game). I has the exact problem in my other computer (one is AMD and the other Nvidia/Intel). I tried to install other games and hadn't any problem.

I tried to update the game (in the other computer) the classic way, downloading the files from the GoG web but there's an error and again the game doesn't update, the patch_log automatically generated says: "File not found (for patching): c:\program files (x86)\gog galaxy\games\no man's sky\\Binaries\NMS.exe".
And if I try to uninstall the game on GoG Galaxy I receive the same message: "Failed installation: problem accessing the disk", I had to do it from windows control panel

I don't understan what it's going on because the day before I played without any problem and the same exact problem occurs on differents pc. I already contacted with the GoG support but I still don't have an answer, so in the meantime, if anyone can help I'd appreciate it so so much. Thanks in advance.

Best thing you have to do is to open a support request, because that is some huge issue you have.

Yeah I know, I already did that, I'm waiting. It's a big problem.

Support ticket is the safe way, aggreed.
In the meantime you can try to get the install (or the patch 1.31 only) via the GOG Downloader. If you still have all installers then I advice you to rip all out and re-install.

Yes, that's odd--probably an ongoing bug-snafu with just-out-of-beta Galaxy relative to configuration, I'd guess. I've just started using Galaxy myself for a few of my games--testing out the autoupdates of games previously installed through the standard non-galaxy front end by importing the already installed directories--and had no trouble at all. Basically, Galaxy is *supposed* to do exactly what the manual installer does--the exact same game is installed--there is no difference in versions or software that I can find (it would make no sense if there were as Galaxy is not required to run Galaxy-installed games--they'll run fine right from the shortcut sans Galaxy), the only difference is that Galaxy theoretically will automate the process for n00bs who need some hand-holding. Likely just a bug relative to Galaxy that you stumbled on, imo. Bad thing about bugs is that the worst of them are intermittent...! Those will drive a man mad!...;)