The installer for 64-bit windows actually ships 32-bit toolchain with 64-bit cross compiler.
I am not sure about the toolchain (make etc), but fpc itself is 64 bit.
I checked some directories and the fpc.cfg file is in the same dir/folder as fpc.exe.
If your fpc is in (32 bit, but similar for 64 bit with change or arch)
C:\lazarus\fpc\2.6.4\bin\i386-win32\fpc.exe
then the fpc.cfg should contain lots of entries with path like either:
-FuC:\lazarus\fpc\$FPCVERSION/units/$fpctarget
-FuC:\lazarus\fpc\$FPCVERSION/units/$fpctarget/*
-FuC:\lazarus\fpc\$FPCVERSION/units/$fpctarget/rtl
or
-FuC:\lazarus\fpc\2.6.4\bin/units/i386-win32
-FuC:\lazarus\fpc\2.6.4\bin/units/i386-win32/*
-FuC:\lazarus\fpc\2.6.4\bin/units/i386-win32/rtl
I would expect NO path to anywhere outside.
NOTE: the fpc dir does NOT need to be in the environment PATH.
I have no idea if the presence of any other fpc install in the PATH may cause issues or not. Same for a mingw install.
The fpc folder should also contain make.exe (and a few others)
There also MUST be either ppc386.exe (32 bit) or ppcx86.exe (or similar / 64 bit)
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from your log
RunFPCVerbose failed: C:\lazarus\fpc\2.6.4\bin\i386-win32\fpc.exe -va compilertest.pas
TFPCTargetConfigCache.Update WARNING: compiler is broken: C:\lazarus\fpc\2.6.4\bin\i386-win32\fpc.exe
What does it say if you run (or whatever path is reported on your failing installation)
C:\lazarus\fpc\2.6.4\bin\i386-win32\fpc.exe -va someunit.pas
where someunit.pas contains
program a;
uses sysutils;
begin
writeln(1);
end;
If you can use fpc like that on the commandline, but not in the IDE, then I suspect your antivirus. Otherwise whatever error you get on the commandline needs to be fixed