use File::Basename;
# ...
while( my @cols= splice @files, 0, 4 ) {
  my @table_cells;
                                                                                
  for( 0..3 ) {
    push @table_cells => $cols[$_]
      ? td( submit(-name=>'file', -value=> basename($cols[$_])) )
      : td( ' ' );
  }
                                                                                
  print Tr( {-align=>'center'}, @table_cells );
}