I also believe that a new PC is your best option. As old as it is, there are any number of parts in yours (such as capacitors on the motherboard) that may be near the end of their working lives.
For playing games, a new graphics card will help, no matter what else you do. Also, a new graphics card would not be wasted money, since you could re-use it in a new build. Considering what you have now, even a GT740 would be a significant upgrade. I would not get anything more powerful than a GT750Ti, as your older processor will bottleneck it, and a stronger card will need a PCIe power cable which you may not have. Note that some, but not all, GTX750Ti cards also need a PCIe power cable. Most do not.