Logic Board or Battery Problem?

I have a MacBook (S/N W8848B) 2GHZ intelCTD, 2G-1067MHZ DDR3. Nvidia GeForce 9400m, running OS 10.5.8

About 5 times in the last month the computer just shuts off. The only consitencies I can find seem to be when i'm watching video and using battery power. Only one time did this happen doing nothing more than opening a folder. The other times I was running multiple software packages, answering email, watching video...stressing the computer out for a good two hours before it seemed to overheat.

The first time this happened, I could not turn the laptop back on. I had to reboot from the disc and rebuild permissions. Every other time the computer has powered right back up.

I have read numerous threads about bad logic boards, however this doesn't seem to be an issue with my laptop serial number. (unless I've missed it in the many, many threads regarding "random" shut downs.) I have not had a shutdown issue while utilizing the AC power cable. This is what leads me to believe it's a battery issue.

I also experience what seems to be a rapid loss of power. My battery time jumps from 2:50 down to 45 within a five minute time frame. 10 minutes later it says 1:45 minutes. I read about the battery update. My update is v. 1.3. apparently what I should be running. My cycle count is at 226, however "condition" states "check battery." not sure what that means.

Any help would be greatly appreciated. thanks for your help.

Jeff