I'm confused by your post because you state that you've been in continuous employment since January 2005 but you haven't made enough contributions during part of this period. If you were an employee (rather than self-employed) your employer should have ensured that your NI contributions were kept up to date. If you were self-employed, your NI payments (Class 2) don't count towards Contribution Based JSA anyway.
Further, if you don't qualify for Contribution Based JSA, you should still be entitled to receive Income Based JSA (which is completely independent of your NI record). The principal exception would be if you had savings of over �16,000. (However, because Contribution Based JSA is means-tested, your partner's income may also come into the equation).
For further information see here
http://www.direct.gov.uk/en/MoneyTaxAndBenefit s/BenefitsTaxCreditsAndOtherSupport/Employedor lookingforwork/DG_10014402
and here:
http://www.jobcentreplus.gov.uk/JCP/Customers/ WorkingAgeBenefits/Jobseekerallowance/index.ht ml
Chris