Edit 6/27/2020: I have switched from the XWA original CDs to the XWA installer from Origin since I have the Basic yearly subscription.
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Edit 4/25/2020: please note, the below instructions have not been updated since 2017. If you need help installing though, please post to ask for assistance. New updated instructions will be made available, but not yet.
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*phew*
After a couple of hours, finally got XWA working again on my Win 10 64 bit PC. And my Gravis xTerminator joystick still worked as it did before! (terribly..)
To make it easy, here is what I did
#1 go to http://markusegger.at/Games and follow the steps in http://markusegger.at/Software/Games/Xw ... tions.html starting at:
#2 From http://xwaupgrade.com/ download page, download the file called "xwa_ddraw_d3d11.1.3.zip" and follow the instructions (easy, copy contents to location where you installed XWA...Create a temporary folder on your hard disk (eg. C:XWA_DISK_1) - about 600 MiB free space is needed.
Copy the contents of your Star Wars: X-Wing Alliance CD 1 to that folder.
Let this self-extracting archive extract to that folder (eg. C:XWA_DISK_1). // NOTE: this is the XWA file you download from the main page http://markusegger.at/Games called Star Wars: X-Wing Alliance 1.0 EN 1.0.0.0//
When asked to replace Setup.exe, confirm.
There should be four new files in your temporary XWA folder:
Alliance.ico
X-Wing Alliance.msi
Setup.exe (new file)
Instructions.html (this file; may be deleted at discretion)
You may create a folder Patches or Support in your temporary XWA folder; you could store the official X-Wing Alliance patch as well as the Windows Installer and C++ redistributable files there.
Burn the contents of your temporary XWA folder (! - not the folder itself) to a blank CD-R and label it accordingly in the CD burning program of your choice (eg. Nero). The original CD label usually is: XWA_DISK_1
Use your new "Installation CD" to install Star Wars: X-Wing Alliance on your computer by either double-clicking on
Setup.exe or
X-Wing Alliance.msi directly.
Obligatory: Install the official X-Wing Alliance v2.02 (or later) patch. You may get it at http://www.lucasarts.com/support/update/alliance.html. // NOTE: I had to get the patch from http://xvt.uharc.net/download:patch using the "mirror de" link. //
To be on the safe side, use your original CD 1 for playing from now on. There might be copy protection or stuff like that.
#3 Insert game CD (yes, the official one you bought about 17 years ago!)
#4 When in game, turn on Hardware 3D or when trying to fly, your game will crash.
Worked for me!

Cut scenes seem a bit slower... currently running a Core i5, 8GB RAM, ATI 6950 video card. Maybe it is the hard drive I installed XWA on that is slow, only 5400 RPM.
Cheers!