You said you wanted to log the errors, not send them to the client. I think the handlers are getting called, and you can log the errors from within them.

If you want to send the error to the client, you'll either need to do some fancy ASP stuff, or use eval BLOCK. For example,

eval {
   ...
   something_that_might_die();
   ...
};

if ($@) {
   # It died.
   # The error message is in $@
   ...
}
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That won't catch division by zero, but it will catch just about everything else. To catch division by zero, check the denominator before dividing.