Hi, I have the same problem with my macbook unibody MODEL A1278. The problem is when one day my macbook won't turn on. Since I'm too bc during that time, i wasn't able to troubleshoot it but instead, i just left my macbook pro in the drawer. After a couple of days i took it out in the drawer and decided to open the button cover, i found out that the battery swell/bulged. so i took it out then put back the button cover and try to turn it on by plugging the magsafe adapter. it works and run for a couple of days, but after 3 days of using it, after turning it on again, i won't turn on and i noticed that the led light on the adaptor becomes dimmed.
I tried many times but still no luck until now. Anybody encountered the same as my problem? your troubleshooting guide will help me a lot to solve my problem. Thanks in advance.