Firmware update-- magsafe still doesn't work

My T-shaped magsafe for my 2008 Macbook stopped working so the people at Apple told me to buy a new T-shaped one. I've done the firmware updates, I've tried resetting the system and the adapter still will not connect. It was working for about a month or two and not it won't connect at all.

Anyone have any ways to fix this problem? I can't buy a new computer for another couple months and I need my computer for grad school.