Macbook Plugged in but not charging

[drmac]

Hello ALL.
Have been facing a very peculiar problem.
Decided to give it a shot here after searching Google for eternity.
I have a white aluminium unibody Macbook from Late 2009.
Model Identifier 7,1
It came preinstalled with Snow Leopard.
I recently upgraded it to Lion. And it was working well.
I was then recommended to install a couple of updates to the computer by the Software Update.
It was an upgrade to version 10.7.3 from 10.7.2 that I had.
Plus, it had an EFI upgrade.
And an iTunes one.
The weird thing is after the upgrade, the MAcbook battery does not charge.
It recognizes the charger and displays, Plugged in, but the battery does not charge.
It started charging once and I let it charge completely, but after that, whenver I plug in MAgsafe, it just shows power source : Adapter BUT the battery is NOT charging.
I have tried resetting the SMC from the Apple support website.
It has not helped.
I am going to try to re-install Snow Leopard, but I doubt it will work coz if it's an EFI problem, it is OS-REINSTALL-PROOF :( !
Please suggest a possible/plausible course of action.
I should mention here that my Magsafe adapter had some problems too.
Like it did not work if the head part was not aligned with the posterior part of the Magsafe Port before, but it used to charge it.
Please offer any insights or suggestions I can try before a "costly" visit to an Apple Store here in India.
Thanks a lot !