The only error I can see is that

print "@data\n"; should have been print OUTF "@data\n";

The coding is actually good, btw - not very idiomatic, so a bit awkward, but you obviously understand what's going on behind the scenes. Nice effort.

The only thing I can see here is I wouldn't open combine.csv every time through the loop anew, and wouldn't slurp the input file into an array.

open(OUTF,">>combine.csv") or dienice("Can't open CSV file: $!");
foreach my $file ( @files ) {
    open(INF,"$file") or dienice("Can't open data file: $!");
    print OUTF while <INF>;
    close(OUTF);
}
close(INF);
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Update: nevermind, the above proposals are better.. duh. :-)

Makeshifts last the longest.