You will go far with a new complete system upgrade, however you can upgrade your current machine for cheaper than a new build. I disagree with most comments made since my last post, as they are incorrect.
It is indeed worthwhile to upgrade your current machine.
First and foremost, thank you for your response and for supplying screen shots of CPU-Z. Please may I ask how much RAM do you have at the moment? Your motherboard only supports DDR2, and you can install 1GB RAM per slot which totals to 4GB system memory. I would recommend you have at least 2GB RAM or above.
Second your motherboard is the
Gigabyte GA-8I945P-G, which not only supports Pentium D processors, it also supports Pentium Dual-Core, Core 2 Duo, Core 2 Quad and Core 2 Extreme CPUs. I am absolutely devastated that other members did not pick this up, you only have to look at the
CPU support list for your model.
You don't need to update your BIOS either to support the Core 2 processors, as you're already on version F8. However regardless I would advise you do, only if you're comfortable with doing so. The latest BIOS version for your motherboard is F11, and it can be downloaded from Gigabyte
here.
At the moment you have somewhat of a weak processor. I would upgrade to the Core 2 Quad Q8300, which is still a solid CPU and costs similar to the weaker Q6600. It's not the best Intel CPU, but for your motherboard it's good enough. You don't want the best CPU for your motherboard either, as they cost more and you'd be better off with a new build if you were to spend that much only on a CPU. The Core 2 Quad Q8300 is a whole lot better than your current CPU, Pentium D's are outdated, to be honest so is the whole Core 2 platform, regardless the performance provided from Core 2 is still great.
Look on eBay for the Q8300, if you're in the United States you can pick one up for around $50. eBay is the best place to look, as the Core 2 processors are no longer sold by retailers; they're that old.
If all your playing is RuneScape however, you don't need the utmost high-end computer. Your current GPU should be sufficient, however it is also obsolete. You could purchase the GTX 750 Ti as suggested by logainofhades, and when you do eventually build a new computer, you could use the GTX 750 Ti in your new build. A GTX 750 Ti will set you back a $150 however. If you want a cheap GPU upgrade, you could look at the AMD R7 250 which costs $75; it's not the best GPU but it's cheap a lot better than your current card.
Please let me know if you do have a budget on how much you want to spend, or ideally how much you were/are planning to spend; perhaps you could do better off with a new computer. Again if you don't already, I would recommend you have at least 2GB RAM or more.
All the best.