$dbh = DBI->connect($dsn, $user, $password,
                             { RaiseError => 1 });

 "RaiseError" (boolean, inherited)
           This attribute can be used to force errors to raise excepti
+ons
           rather than simply return error codes in the normal way. It
+ is
           "off" by default.  When set "on", any method which results 
+in an
           error will cause the DBI to effectively do a "die("$class $
+method
           failed: $DBI::errstr")", where $class is the driver class a
+nd
           $method is the name of the method that failed. E.g.,

             DBD::Oracle::db prepare failed: ... error text here ...

           If you turn "RaiseError" on then you'd normally turn "Print
+Error"
           off.  If "PrintError" is also on, then the "PrintError" is 
+done
           first (naturally).

           Typically "RaiseError" is used in conjunction with "eval { 
+... }"
           to catch the exception that's been thrown and followed by a
+n "if
           ($@) { ... }" block to handle the caught exception. In that
+ eval
           block the $DBI::lasth variable can be useful for diagnosis 
+and
           reporting.  For example, $DBI::lasth->{Type} and
           $DBI::lasth->{Statement}.
[download]

I could be way off. But often you can innoculate your script from the grim reaper of death by trapping him inside an eval. ;)

you can use raiseerror
you can use warn if you want to raise a connection alert but do not want to exit.
you can have a "crude implementation" of pinging the server and using a if ( my $output =~ m/ping positive output on your operating system) { query }.
HTH