I don't think Tomte's solution is clugy at all (and I really like Albannach's version of it). Another possibility that might work for you, depending on what the data really look like, could go like this:

{
  local $/ = "request(";  # change the input record separator

  while (<>) {
     if ( /^(.+)\s+START_TIME, (.*)/ and $1 ne "BADSTRING" ) {
        print "$1:$2\n";
     }
  }
}
[download]

This assumes that the data stream is a series of records that all start with "request(" and have line breaks as indicated in your example (because /(.*)/ does not match a new-line character). But if your data varies from that a bit, it might still be pretty easy to adapt this idea to handle it.