I'd recommend chumming up with another Mac owner with a similar sized MBP, loaning their power brick and testing it out. If both act the same, could be that the MagSafe socket is damaged and will require costlier repairs, else you'll have to do as Prof. Kappy states. But it is better to be sure first.
I am sure that the issue is not a busted MagSafe port. From my observations, the light of the LED indicator turns off (completely) when you wiggle the cable that goes from the adapter to the computer. If you wiggle the cable again the light turns on and supplies power to the computer. I am deducing that the cable that goes from the adapter to the computer is broken. Furthermore, the changes in the MagSafe LED lights when the cable is wiggled occur while the MagSafe plug is connected to the computer.
Also, given that this is my college computer which I use for notes and classwork how ca in work around this issue until I save up to buy the adapter in the following weeks? Should I leave the computer unused? In other words, what stop gap measures should I take to get by the following weeks?
Ah, this is for the dancing charge lights: http://support.apple.com/kb/HT3205
Make sure the plug and socket are absolutely clean and the connector goes in flush. See especially #7 & 8 (click on triangle to open): http://support.apple.com/kb/TS1713
And of course, there's always social engineering: select a suitably equipped classmate to sit next to, do an anguished puppy dog look, bum their charger's plug and juice up yours till the piggybank fattens up enough...
I did followed the suggestions outlines in the article and the MagSafe head is clean. The same case is found the MacBook Pro MagSafe port. The behavior of the battery LED lights are normal and do not show signs of problems. I think it all boils down to a problem with the MagSafe cable that goes from the Power Brick to the computer.
As for the social engineering thing, I think I am the only person with a 15 inch MacBook Pro. The only macs that I've seen are 13" MacBook Airs and Pros and there are only 4 students with macs in my study program (I attend a small size college).
Again thanks for the help. Probably, I just was the victim of bad luck with a weak MagSafe power adapter. The replacement will have to wait till November as I save up for a purchase.
Thanks for your time!