Whenever you use system commands, you will want to make sure you check the exit status. Additionally, the error is stored in $!, and should give you an idea of why things are failing. Try something like this:

open(OUT,">outfile") || die;
for($i=0;$i<=$#bigfile;$i++){
  $bigfile[$i] =~ s/\0/ /g;
  print OUT "$bigfile[$i]";
}
close(OUT);
print "Compressing original file\n";
system("compress original.file")
  and die "Unable to compress data: $!\n";

print "Concatenating other data\n";
system("cat ./incoming/data.file ./static/data.file >> outfile")
  and die "Unable to cat data: $!\n";

print "Sorting Data File\n";
system("asort outfile clean.data 1 6 8 9")
  and die "Unable to sort data: $!\n";

print "Done.\n";
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You may also want to use system in a list context, as it is faster and more secure, for example:

system("/path/to/asort","outfile","clean.data","1 6 8 9")
  and die "Unable to sort data: $!\n";
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Lastly, your for loop isn't very perlish. You may want to try something like this:

open(OUT,">outfile") || die "Unable to open outfile: $!\n";
foreach (@bigfile) {
  s/\0/ /g;
  print OUT "$_";
}
close(OUT);
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Cheers,
Shendal

Update: As runrig pointed out via the chatterbox, it ought to be and die after a system, since system returns 0 on success.

Update2: See merlyn's post RE: Re: large file issue?. $! is actually not what you want to look at.