macbook pro 13'' in mid 2009; shutdown and power cable issue

I bought this macbook pro 13'' in mid 2009, running snow leopard. Its been running smooth until a few weeks ago.

My mag safe power cable wasn't lighting up properly for months beforehand, I thought this was a battery issue, and those suspicions were confirmed when I got a 'replace battery now' message. I've just been to the Genius bar where they replaced the battery, and I left thinking I had a fixed computer.

My power cable still won't light up properly. I now know that I've been putting unnecessary stress on the cable.

What prompted me to post on this forum was the following situation that just occurred. I was watching a movie with the battery half charged, unplugged from the power cable, when my computer completely shut down for no reason. As I hit the power button, it made a few strange clicking noises. (I was very afraid at this point) When I reattached the cable and tried again, it did start up BUT the Date/time was reset to January 1, 2008 and I had to reconnect to the WiFi network.

Question 1: Will using this semi- broken power cord do irreparable harm to my machine? to my battery? Should I replace it immediately?

Question 2: What caused this shutdown? I assume it a power connection problem but I'm just not sure.

I'm at your mercy, Gods of Mac. May you show me your good favor, and solutions that are less expensive than most.

Answers

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My computer has been having this issue recently. I don't know what the problem is or how to fix it.
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