pattern match problem got me stumped, and if possible I would like to know how its done? You are very close. You need to stop capturing Status at the end of the line with \n and then need to allow any number of other characters before the "Last Result:" tag. See below.
Few other points, there is no need to mess around with $1,$2. Use list context on the left hand side and assign directly to the variables that you want. The regex matched if the rightmost of the variables is defined; in this case $result.
use strict;
use warnings;
my $out = do {local $/; <DATA>};
my $task = 'infiniteloop';
my ($status, $result) = $out =~ m/TaskName:\s+$task.*?Status:\s+(.+?)\
+n.*?Last Result:\s+(\d)/s;
print "status = $status\n"; # status = Running
print "result = $result\n"; # result = 0
__DATA__
HostName: LAP3220889
TaskName: infiniteloop
Next Run Time: 11:06:00, 23/06/2011
Status: Running
Last Run Time: 10:10:04, 23/06/2011
Last Result: 0
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