This isn't the right place for hardware recommendations, but I'm going to answer this because I think it's unfair to automatically throw out hardware based on age and build a new machine in every scenario. That's not to say you should keep old machines forever; it depends on the workload. This is that part that will attract opinionated answers as if it's worth upgrading or just starting anew; I'm going to answer the question from a fairly simple standpoint because of that: what you can do, not if you should. I'd say because of the extremely low marginal cost, it might be worth it. But that's my opinion.
Your motherboard supports up through the highest Core 2 Quads; this should provide a much needed bump in CPU performance. Cheap C2Qs like the Q6600 can be found for under $10, and 771 Xeons are often even cheaper while overclocking better and can be used with many 775 motherboards with some modification. They won't compete even clock-for-clock with modern processors because of IPC improvements, but they can still tow their weight in games, and will be plenty fine in light productivity. Depending, add a GPU of reasonable caliber (I wouldn't go above a GTX 1050/RX 460.)
Get 4-8GB of DDR2 depending on your needs. Just productivity? 4GB is probably fine. Gaming? 8GB maybe what you want. Note for the latter you'll need 4GB sticks because your motherboard only has two slots. The biggest challenge here will be finding 4GB sticks of DDR2; while there's plenty of ECC DDR2 in that size, finding desktop memory in that size may be quite a challenge.
Good luck in your ventures.
