Ms Anderton, 29, was left in tears when none of the male contestants chose her.
BBC: NEWS | Entertainment | Low ratings for ITV's Love Island
Anderton, like Cole, missed out on a trip to Holland and Belgium due to an ongoing injury.
And through a combination of Gronkjaer's trickery on the wing and Anderton's quick feet, Birmingham were soon level.
BBC: SPORT | Football | Premiership | Blackburn 3-3 Birmingham
"There's a very important few months ahead for the club and we'll just see how things go, " Anderton said.
From the restart, Darren Anderton delivered a deep cross from the right, but Jaaskelainen gathered comfortably despite Emile Heskey's challenge.
Former manager Burley left Hearts in October by "mutual consent" before ex-chief executive Anderton was sacked after a boardroom disagreement.
BBC: SPORT | Football | My Club | Heart of Midlothian | Romanov lashes out at sacked trio
Darren Anderton and Gus Poyet struggled to win possession for Spurs, leaving front pair Freddie Kanoute and Robbie Keane horribly isolated.
The Trinidad international was roundly booed by fans as he warmed up and in particular when he replaced Darren Anderton as substitute.
BBC: SPORT | Football | My Club | Birmingham City | Yorke 'racially abused' by fans
Model Sophie Anderton, and actor Lee Otway are taking part this year.
BBC: NEWS | Entertainment | Low ratings for ITV's Love Island
But Anderton stressed that the club's new owners would be demanding employers.
When an interactive ad shouts out to Tom Cruise's character in the 2002 film Minority Report: "John Anderton, you could use a Guinness!"
Gronkjaer picked out Anderton in space in the middle and the former Spurs midfielder quickly moved the ball out to the marauding Melchiot.
BBC: SPORT | Football | Premiership | Blackburn 3-3 Birmingham
Birmingham got their reward when Clinton Morrison acrobatically turned Anderton's corner onto the crossbar, and Upson reacted sharply to bundle home the loose ball.
Birmingham drew level on 16 minutes through Darren Anderton's close-range finish and Mario Melchiot then set up goals for Robbie Savage and David Dunn.
BBC: SPORT | Football | Premiership | Blackburn 3-3 Birmingham
Shearer and Darren Anderton were narrowly off target from long range.
Foulkes, the then chairman, resigned in protest at Romanov's treatment of Anderton, but Lithuanian millionaire Romanov insists that he had no choice but to ring the changes.
BBC: SPORT | Football | My Club | Heart of Midlothian | Romanov lashes out at sacked trio
Standing in his way are those four summer captures - Jamie Redknapp, Milenko Acimovic, Jonathan Blondel and Rohan Ricketts - not to mention the likes of Gus Poyet and Darren Anderton.
Robertson was a Hearts hero as a player and only took over from Craig Levein this season, while former Scottish Rugby Union chief executive Anderton has only been in post for 10 days.
Hollands and Gowling are out of contract at Dean Court this summer, as are defender Ryan Garry, versatile duo Shaun Cooper and Lee Bradbury, captain Darren Anderton, midfielder Marvin Bartley and striker Brett Pitman.
Working down the left, Gronkjaer found Dunn with an astute pass and although the former Blackburn player's touch let him down, the ball fell to Anderton who deftly tucked his shot into the corner.
BBC: SPORT | Football | Premiership | Blackburn 3-3 Birmingham
And despite padding out the action to a buttock-numbing running time with some unnecessary sentimental nonsense about Anderton's estranged family, he reminds us that few living directors can spin an escapist yarn quite as well as he does.
Cruise is on top form here, and there is nice work from Irish actor Colin Farrell as his right-hand man, and Samantha Morton as the android-like "pre-cog" who predicts future murders and might just hold the key to Anderton's innocence.
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