What's the while inside while code you tried? (we can advise if it's minor to fix or a compare it to other solutions.)

As for other solutions, the first question i think is if you can slurp in the whole log file or not. Assuming you can't due to size, you were on the right track with a while loop... perhaps something like:

while(my $s1 = <LOG>){
  next unless $s1 =~ m#^(\d+/\d+/\d+) (\d+:\d+:\d+) user=(\S+) func\(#
+;
  my ($date, $time, $user) = ($1, $2, $3);
  ...  # above variables are available
  while(my $s2 = <LOG>){
    last if $s2 =~ /^\) #end trans#/;
    ...   # $s2 is log data
  }
}
[download]

Note you could do this w/a single while loop (as opposed to nested ones) if you used a boolean or two to keep track of being inside a log data section or not..

Update: I like the above solution of $/ = '#end trans#' -- my original thought was to split() on the start line, but that would required the whole log in memory, so i switched back to the while/while method.. hopefully it will at least serve as a guide is debugging your while loop attempt.