power adapter green light no power no charge

Thanks in advance for any help with this; I'm a Peace Corps Volunteer currently serving in rural Cambodia, so it's a little tougher to deal with this problem and/or get an alternative computer.

I had been using my MacBook when I realized that although it was plugged in and the LED was green, the battery was losing charge. I tried cleaning out the connector and magsafe port and doing some other trouleshooting including trying to reset the PRAM and SMC. Eventually I was able to borrow a different adapter from a friend, and that didn't work either, so I know it is not an issue there. At this point, the battery is completely drained, and although the LED still lights green (and sometimes orange for a few seconds after being plugged in), the computer will not turn on at all even when plugged in, so it is not just a battery issue. I've been fiddling with it for about a week and no luck on anything. Other than this problem, everything seemed to be working completely fine until the battery died. From some reading, I'm wondering if the problem may the logic board. If so, does anyone know how much it would cost and how long would it take to fix that problem? Are there any other possible things it could be? I'm in a situation where, luckily, there is an Apple repair place in the capital city, but I can only be there for short periods of time once in a great while. I also don't have access to a whole lot of cash and would need to plan in advance if it will be pricey. My Mac has been great until now and is the way I Skype with family and friends, save photos, watch movies, etc from my Peace Corps village, so it would be really great if I could get it fixed. Thanks for any help!