You have RaiseError set, which in the Unix world, would mean any error from DBI will go to stderr and with Apache they would end up in the apache error log (but in any case, if there were a problem with the DBI->connect(), your example would die before it printed any DBI error to your logfile). I don't know where error output ends up on IIS, but I would try something like this to make them go where you want them to:

eval {
  my $dbh=DBI->connect("dbi:ODBC:$DSN",'USER','PASSWORD',{ 
             RaiseError => 1, 
             AutoCommit => 1,
             PrintError => 0 } );

 # More database stuff create statements, execute
};
if ($@) {
 print LOG $@;
 exit;
}
print LOG "Good\n";
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