power cord not working

Due to a prematurely failing battery, I was just sent a free replacement. The battery's fine, but ever since I installed it, my power cord hasn't worked- the LED doesn't turn any color, and it's not charging the computer. I even tested it with my old battery and it still didn't work (when it had worked with that battery five minutes prior), nor would it work on a friend's laptop (but their cord worked fine on my computer). I also tried resetting the SMC to no avail.

Since it's obvious that the problem lies with my (over a year old, fraying) AC adapter, should I just buy a new one, or is there anything else I can try? It's just odd that it would stop working at that exact moment, when it's been working even in its fraying condition for quite a while now.