Macbook Pro 15" late 2008 random improper shutdowns on battery

Question

Hi, my macbook pro 15" late 2008 model shuts down by itself when on battery. The problem started one day out of nowhere about 2 months ago. There seems to be no recurring pattern in the shutdowns as I can sometimes use the computer for one or two hours, sometimes only 5 minutes before it shuts down. The computer works perfectly when the charger is plugged in, and also when the battery is pulled out and only the charger is plugged in.
Here is what I've done so far:
Reset of the SMC
Reset of PRAM
Repair of hard disk and disk permissions with Disk Utility
Reinstallation of Snow Leopard 10.6.3 from disc and then install of all software updates
Reinstallation of all updates with the downloadable Combo Update
None of this fixed the problem.
I am a student in Glasgow, but normally live in Luxemburg. When I went back to Lux for the holidays I sent the mac for repair at Lineheart Luxemburg. The first time it was returned to me after a week. They hadn't detected the problem because they had only ran the tests with the charger pluggged in. I was quite annoyed as you might understand. All they told me was to buy an 85W charger for the mac as I only had a 60W one. This is my uncles old computer and I don't know why he had the wrong charger. I got the computer a year ago and it had worked flawlessly until now. The 85W charger didn't fix my problem.
I sent the mac back to Lineheart and they ran a second test for free. They found the problem and all they did was to repair the hard drive with Disk Utility and reinstall Snow Leopard 10.6.3. WHICH I HAD ALREADY DONE MYSELF. This time I was really annoyed. The problem basically occured again straight after I went to get the computer.
Now I am back in Glasgow and I have an appointment at the Genius Bar tomorrow. I hope they can be of a bit more help although the people at Lineheart are "Apple Mac Certified Technicians" too. I've already spent 140€ for nothing.
All I really want is to test the computer with another battery since the problem seems to really come from there. However none of the technicians did this and I don't have any friends with a similar model of Macbook.
The cycle count is at 263 and the status is "normal" for the battery.
There is a weird problem though, when I plugg in the charger the icon on the top right will first say "not charging" if I unplug the cable at this moment the computer dies. If I leave it in for about a minute it will start calculating the time until full charge. This takes MUCH LONGER than it used to and when it's done I get something silly like 20 hours or 6:30 hours until full charge. After 5-10 minutes it starts calculating again. After a long time I get something more sensible like 1:30 or 2 hours until full charge. Notice that during this entire time, the percentage of the charge will not have change by a single percent. It can sometimes take up to an hour until the battery actually starts charging.
I've read on different forums that this can be related to the logic board and then my Macbook will just have to become a stationary computer since I can't pay 1200€ to get the logic board replaced. I really hope I just need battery replacement.
Also, after I turn on the mac again after an improper shutdown my antivirus (avast!) will give me a message "An internal error has occured. You can find more information in the system logs. After filtering for shutdown this is what I found. (sorry for the screenshot, I couldn't find how to copy the log)
Sorry for this very long description but I wanted you to have all the information. I'm really getting desperate so any help is appreciated even if it's only on how to locate the problem I would be so gratefull. Thank you all.
Daniel Lecoq

Answer 1

Yes, I boot up from the OS 10.6.3 installation disc and use Disc Utility to repair Disk and Permissions. I must tell you though, I've done the disc repair and permission repair quite a few times and it has never helped. Right now I've forgotten the OS disc in Luxemburg so I can only get it when I'm back in 3 weeks.
I ran Disc Utility today though and repaired permissions. The only one that wasn't fixed was an SUID-file.
I also checked the disc and it has some problems but I can't fix them until I get my OS disc or if I ask them to do it at the Genius Bar.
Yes, I have a Time Machine backup on an external usb HDD, last time I backed up was yesterday.