In case Forestidia would still like to build again and produce an allegro.log file (I don't think we need it anymore, though): I've tried once again to pack debugging DLLs and LIBs, see attachment. Maybe I made a mistake earlier.
I doubt this is useful anymore because we're on a good track. I attached this merely for completeness.
I've tried it but I needed some DLLs that are contained in a MinGW-distribution on top of that (e.g. libwinpthread-1.dll). With adding them it ran and gave me the allegro.log. (The crash window message comes from Microsoft Visual C++ Runtime Library.)
The error seems exactly there where ccexplore suspected.
Log for taskbar crash (Win 7) (I've shortened the path for the Lix root directory.):
stdio D file_stdio.c:109 file_stdio_fopen [ 0.00000] opening C:\...\LixD-master\bin\allegro5.cfg r
system W wsystem.c:792 _al_win_safe_load_library [ 0.00000] PathFindOnPath failed to find shcore.dll
system D wsystem.c:788 _al_win_safe_load_library [ 0.00000] PathFindOnPath found: C:\Windows\system32\user32.dll
system D wsystem.c:699 load_library_at_path [ 0.00000] Calling LoadLibrary C:\Windows\system32\user32.dll
system I wsystem.c:702 load_library_at_path [ 0.00000] Loaded C:\Windows\system32\user32.dll
system I system.c:263 al_install_system [ 0.00000] Allegro version: 5.2.3
dtor D dtor.c:196 _al_register_destructor [ 0.00014] added dtor for timer 000214E8, func 696363E1
dtor D dtor.c:196 _al_register_destructor [ 0.00697] added dtor for queue 0002FB00, func 69625C77
dtor D dtor.c:196 _al_register_destructor [ 0.00704] added dtor for queue 0002FB80, func 69625C77
audio-dsound I dsound.cpp:255 _dsound_open [ 0.00707] Starting DirectSound...
audio-dsound D dsound.cpp:264 _dsound_open [ 0.02727] DirectSoundCreate8 succeeded
audio-dsound E dsound.cpp:269 _dsound_open [ 0.02733] SetCooperativeLevel failed: DSERR_INVALIDPARAM
audio E audio.c:23 _al_set_error [ 0.02734] No audio driver can be used. (error code: 1)