Storm, 28, was a team-mate of Luke Donald and Paul Casey at the 1999 Walker Cup.
Britons Paul Casey, Justin Rose, Martin Laird and Ian Poulter all made the cut.
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Ryder Cup winners Paul Casey, Miguel Angel Jimenez and Lee Westwood will make the trip to Ireland.
Weybridge's Paul Casey (70) is one under at Carton House, while Ulster's Darren Clarke (70) is one over.
Mickelson ended alongside Ernie Els, Dustin Johnson and Ryo Ishikawa with Paul Casey in a group at even par.
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Paul Casey (68) is eight shots off the lead, while Ireland's Paul McGinley (68) is a shot further back.
This week then was the last opportunity for Padraig Harrington, Paul Casey, Justin Rose, Luke Donald and Sergio Garcia.
Britain's Paul Casey, Lee Westwood and David Howell all need a good finish.
Gonzalez produced a final-round 65 to win by one shot from Paul Casey, Padraig Harrington, Nick O'Hern and Marten Olander.
European number one Montgomerie will face strong competition from holder Miguel Angel Jimenez and Ryder Cup duo Paul Casey and Thomas Bjorn.
Defending champion Paul Casey was five shots off the pace after two birdies on the back nine left him on one under.
Last week's Abu Dhabi winner Paul Casey made an indifferent start, carding a par 72, while Ireland's Paul McGinley finished at one under.
Kenny Perry, Boo Weekley, JB Holmes, Ben Curtis and Chad Campbell were the other American victors, while debutant Hunter Mahan halved with Paul Casey.
Westwood produced a solid one-under-par round to stay in contention at nine under par overall while fellow Englishman Paul Casey is a further shot back.
But team-mates Paul McGinley, Thomas Levet and Paul Casey, who were all due to play, have opted to rest after their heroics at Oakland Hills.
England's Robert Rock shot 69 to be level with McIlroy, while compatriot Paul Casey carded 66 to be equal fifth with Scotland's Paul Lawrie (73).
Fellow Englishmen Paul Casey and Ian Poulter went out of their way to avoid watching the whole statement by Woods as they concentrated on their matches.
England's world number nine Paul Casey, the joint first-round leader, was still the highest placed Englishman going into the weekend after carding 73 to finish level par.
Montgomerie gambled on the 39-year-old Dubliner as one of his three captain picks, ahead of more conservative options such as world number seven Paul Casey and Justin Rose.
Darren Clarke and Paul Casey also hit rounds of 68 to move to 10 under while Paul McGinley is seven under for the tournament after a one-under-par 71.
With only nine players in the 54-strong field under par, the Ryder Cup trio of Paul Casey, Padraig Harrington and David Howell are firmly in contention on level par.
Lee Westwood and Paul Casey are one shot further behind at six-under with a third Englishman Steven Tiley also on that mark after 10 holes when play was called off.
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The veteran shot five birdies and three bogeys to lay alongside England's Paul Casey, while Spain's Miguel Angel Jimenez and Retief Goosen of South Africa are well placed on three under.
Paul Casey, David Howell, Retief Goosen and Bradley Dredge are among those one further back, but Colin Montgomerie is down on three under and in danger of being an also-ran yet again.
Paul Casey, still battling the rib injury which sidelined him for three months, Volvo World Match Play Championship winner Ross Fisher and Martin Kaymer, who is still struggling with a foot injury, sit on four-under.
Over half of the 2004 Ryder Cup team - Paul Casey, Darren Clarke, Sergio Garcia, Harrington, David Howell, Ian Poulter and Westwood - have hardly been spotted on the European Tour so far this season.
Fisher, who lost to Paul Casey in the semifinals of the Accenture World Match Play in Arizona in February, had a nervy finish after seeming to be home and hosed at two-up after 28 holes.
Yet Oosthuizen left Paul Casey, Lee Westwood and the world number one Tiger Woods in his wake, with his final round of one-under-par 71 giving him a 16-under total of 272 and his only major title so far.
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