After looking through the available BIOS updates, it shows no need for an update to support a C2Q. There's actually a version that comes with the Core 2 Quad Q8200. The chipset SHOULD be the Intel G43, not the G35. Have you upgraded the motherboard at any time? Are you sure about your assumptions of the chipset? Expect a pretty hefty price tag when upgrading to a 775 socket quad core, the cheapest I have found (not searching a whole lot), was $180... If you're looking to do that, I would HIGHLY suggest a new motherboard and a Phenom II X4 955 (Black Edition, highly overclockable), or Athlon II X4 640/645.
To get a decent gaming PC, I would suggest upgrading to a quad core, and a new graphics card. The 9500GT is nothing in recent games basically, expect to be in the LOW FPS, with LOW details on most newer games.
My upgrade suggestions :
Newegg.com - AMD Phenom II X4 955 Black Edition Deneb 3.2GHz 4 x 512KB L2 Cache 6MB L3 Cache Socket AM3 125W Quad-Core Processor HDZ955FBGMBOX (If it overclocks anything like my unlocked cores Phenom II X2 555, essentially the same since it's unlocked to a quad, it'll be a beast for any game you throw at it. Even if it doesn't overclock that well, you don't need to worry 'cause it will still run great!)
Newegg.com - ASRock N68C-S UCC AM3/AM2+/AM2 NVIDIA GeForce 7025 / nForce 630a Micro ATX AMD Motherboard (I chose this, 'cause it will use your DDR2 (Only 4GB of it though) you have now, and you can upgrade to DDR3 (up to 8GB) when funds become available)
= $160 + shipping
With a new graphics card
Newegg.com - AMD Phenom II X4 955 Black Edition Deneb 3.2GHz 4 x 512KB L2 Cache 6MB L3 Cache Socket AM3 125W Quad-Core Processor HDZ955FBGMBOX
Newegg.com - ASRock N68C-S UCC AM3/AM2+/AM2 NVIDIA GeForce 7025 / nForce 630a Micro ATX AMD Motherboard
Newegg.com - SAPPHIRE 100297L Radeon HD 5830 1GB 256-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card w/ ATI Eyefinity Technology
= $270 + shipping
That compared to a $180 CPU only, and sub-par graphics, I would definitely go with the new motherboard, CPU and GPU, if the funds are available.
Your 9500GT currently ranks #72 on our (T-F's) Graphics Performance List. The 5830, which isn't listed in the Graphics Performance List, performs roughly around the same of a 4890, which is ranked 22.