Is every field in quotes, then? If so, you might be able to read lines until you match quote-newline at the end of a line, strip the leading and trailing quotes, then split the whole mess on /",\s*"/. Like so (untested):

my $line = '';
my @fields;
while (<>) {
    $line .= $_;
    if (/"\n/ or eof) {
        $line =~ s/^"//;
        $line =~ s/"$//;
        @fields = split(/",\s*/);
        $line = '';
    }
}
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