Strange Dell Latitude D530 random shutdowns

Hello there! Recently I have been having an issue with my Dell Latitude D530 as already stated by the title...the laptop will decide to randomly shut down. I have opened the machine and the RAM stick that can sometimes fall out of place by accident is in the laptop solidly, I have checked over the motherboard to ensure that nothing is wrong and found nothing wrong with it, the computer is kept very clean as well as running Vista Business SP2 on an 80 GB Intel SSD which more than rules out a performance issue, and the heatsink was blown out with a can of air a week ago (the laptop's RAM gets warm but never gets to a concerning temperature of any kind) which rules out the overheating situation. I feel I may be having an issue with my battery, as when the battery is a little bit warmer than room temperature and charged between 45% and 60% battery, the computer will completely lose power if the CPU usage exceeds 80%. This is quite an obvious diagnosis, of course...but the second D530 I had for spare parts got fixed up by my little brother a couple of months ago. I don't exactly have any way to make $50-70 bucks at the moment for a replacement and was curious to know if there's any other potential causes of this issue aside from what I have already ruled out even if they aren't specific to this model of laptop. Thank you for your help.