For anyone wondering, I deleted my BGLMANX.DLL and the corresponding .DAT file and it worked perfectly!
That's not possible. First, because without a bglmanx.dll running (and of course its .dat files) GSX won't even start so, you surely haven't done that.
If, instead, you meant that you did that, but then you reinstalled GSX and it started to work, the problem is likely that you had another external program (like an antivirus) which *blocked* the installation of the correct bglmanx.dll and bglmanx.dat files that comes with the GSX installers (and are download online), so after you manually removed them, the installer could complete.
The interference from a security-related product like an antivirus or similar, could also explain why you reported errors accessing the activation servers, which have been fixed since a couple of week by now.