There should be more information after MacBook Pro on that site that will exactly identify the model. From the processor speed you gave, it should read MacBook Pro (15-inch, Late 2008) or MacBook Pro (15-inch, 2.53 GHz, Mid 2009) or MacBook Pro (15-inch, Mid 2010). I am going to assume you meant MacBook Pro (15-inch, 2.53 GHz, Mid 2009).
Since there aren't any user-serviceable parts inside your Mac, you can easily cause static damage by opening the case and touching the internal components directly without the proper anti-static setup. In addition, simply feeling the temperature of the chips on the logic board doesn't identify those that may possibly be overheating or operating outside their design range. They can easily reach various or "untouchable" temperatures during normal operation. The cooling fans work in conjunction with the aluminum housing to dissipate heat. If it is a true overheating situation, normally the entire system would power off to prevent damage. Since your fans continue to work and the system stays powered on, it could simply be failure of individual components. Because the chip is soldered to the logic board, it does indeed sound like the video memory. It is not a component-level repair - it would require a replacement of the entire logic board.
Without additional diagnostic test results, it would be impossible to determine the actual cause of the issue. You could try
Using Apple Hardware Test to see if that will identify any issues, or take it into an Apple Store or third-party Apple Authorized Serve Provider for full hardware diagnostics.
We don't recommend investigating internal issues like this without the proper training/certification, as you can cause damage to your Mac or loss of data.
Hope that helps,
C
