Perhaps it would be better to use a real parser like Parser::RecDescent.

Also please wrap code fragments in your post into <code></code> tags

See the gen_delimited_pat method in Text::Balanced.

Your post would be clearer if you used <code>...</code> tags around your code and data. (You can still go back and add those I think.)

I'm guessing at the real format of your input data, since I think you might have two lines run together. The following might do what you want:

#!/usr/bin/perl -w
use strict;
use warnings;
use diagnostics;

my @lines = <DATA>;
check3($_) foreach @lines;

sub check3
{
    my ($str) = @_;

    if ($str =~ m{
        ^                       # Beginning of line
        \s*                     # optional space
        constant                # "constant"
        \s+                     # required space
        (fixup|/\*fixup\*/|)    # "fixup" or "/*fixup*/" or "" (captur
+ed)
        \s*                     # optional space
        (private|)              # "private" or "" (captured)
        \s*                     # optional space
        (\w+)                   # type/typedef name (captured)
        \s*                     # optional space
        =                       # "="
        \s*                     # optional space
        (?:                     # grouping 1 start
            (?:                     # grouping 1.1 start (U1 format)
            <                       # "<" start of U1 format
            ([[:alnum:]]+)          # part a" of U1 format     (captur
+ed)
            \s+                     # required space
            ([[:alnum:]]+)          # part b of U1 format      (captur
+ed)
            >                       # ">" end of U1 format
            )                       # grouping 1.1 end
        |                       # or groupings 1.1 & 1.2
            (?:                     # grouping 1.2 start (filename for
+mat)
            "                       # Filename start quote
            ([[:alnum:]_/\\\.:]+)   # Filename  (captured)
            "                       # Filename end quote
            )                       # grouping 1.2 end
        )                       # grouping 1 end
        \s*                     # optional space
        (?:                     # grouping 2 start
            /\*\s*(.*?)\s*\*/       # "comment" or undef     (captured
+)
        |                       # or
                                    # blank
        )                       # grouping 2 end
        }x
        )
    {
        print "3: MATCH\n";
        my ($fixup,$private,$name,$u1a,$u1b,$filename,$comment) = ($1,
+$2,$3,$4,$5,$6,$7);
        print "fixup=\"$fixup\" ";
        print "private=\"$private\" ";
        print "name=\"$name\" ";
        print "u1a=\"".(defined $u1a ? $u1a : "undef")."\" ";
        print "u1b=\"".(defined $u1b ? $u1b : "undef")."\" ";
        print "filename=\"".(defined $filename ? $filename : "undef").
+"\" ";
        print "comment=\"".(defined $comment ? $comment : "undef")."\"
+ ";
        print "\n";
    }
    else
    {
        print "3: Sorry Charlie\n";
    }
}

__DATA__
constant fixup private AlarmFileName = "C:\TMP\ALARM.LOG"
constant fixup ConfigAlarms = <U1 0> /* U1 Format */
[download]

Here's the output I get:

3: MATCH
fixup="fixup" private="private" name="AlarmFileName" u1a="undef" u1b="
+undef" filename="C:\TMP\ALARM.LOG" comment="undef" 
3: MATCH
fixup="fixup" private="" name="ConfigAlarms" u1a="U1" u1b="0" filename
+="undef" comment="U1 Format"
[download]