There are various different Core 2 Quads available you can purchase used (you can't purchase them new, since they're discontinued). Therefore you could always upgrade your processor to a better Core 2 Quad, but to be honest with you, I would not bother upgrading to another Core 2 Quad since they are old tech. The motherboard in your friend's build will not be capable of accepting any new processors, since it is on the old 775 socket. Hence if you want to upgrade the CPU to something more modern, you'll need a new motherboard; you will NOT need new RAM modules since your friend's build includes the still mainstream DDR3. You can transfer the existing RAM to a new motherboard.
Could you please download and run
CPU-Z, once open select the "Memory" tab and please reply back with the "DRAM Frequency"? I am attempting to verify that you can indeed use your existing DDR3 RAM with a new motherboard.
I would purchase your friend's system for $100; it is a great deal. Heck, I'd pay more than $100 just for the GTX 660 Ti graphics card.
Is the hard drive in your friend's system SATA or IDE/PATA by the way? Since the motherboard does support both. Ideally you want it to be SATA; if you upgrade the CPU, you need to upgrade the motherboard whereby modern motherboards do not support IDE/PATA. (IDE/PATA are obsolete.) If the hard and optical disc drives are IDE, then you'll need to purchase new SATA hard/disc drives for a new motherboard; hence why if they are already SATA, you can simply move them over to a new motherboard which supports better processors.
Finally for the last of questions, what brand/manufacturer is the power supply? It's important to have a decent quality PSU, especially on an older system such as the Core 2 Quad, since perhaps the PSU has deteriorated over the years.
Now, why have I assumed that replacing the motherboard and CPU would be your best option here? Your friend's motherboard which runs the Core 2 Quad is old, heck even the Core 2 Quad is old; they're both obsolete. The other components are worth keeping, if the HDD/ODD are SATA, the RAM is at least 1033MHz (I will determine this after you provide the DRAM Frequency after running CPU-Z), the power supply if it is produced by a decent manufacturer, and most definitely the GTX 660 Ti (the GTX 660 Ti is even better than my current card).
If you replace the motherboard and CPU, yet keep all the other components; then you may just have earned yourself a major bang for you buck. I'll attempt to assist you in finding the best deals.
So if possible, please reply back with the DRAM Frequency of the current RAM in the system, if the HDD/ODD are SATA or IDE and the brand of the PSU. I'll try and find you a suitable upgrade to the processor and motherboard; I was thinking perhaps upgrading you to an Intel i5, which is solid for gaming and will perform even better tied in with the GTX 660 Ti.
All the best.