>What if I upgraded to the highest performance processor that I could, without buying a new motherboard.
Motherboards can only accept a certain "range" of CPUs. So it is not about buying the best CPU you can, it is about buying the best processor your motherboard can take.
But the speed of a CPU is only part of what makes a PC go fast. It is also about the speed of the memory, the speed of your hard disk, and the speed of your BUS (the speed the data flows round your motherboard).
So you could maybe get a CPU that was twice as fast as your current one, but the PC would not go twice as fast, maybe only 20% faster or whatever.
As technology moves on the speed of everyhing increases. CPU speed gets better, memory speed gets better, BUS speed gets better. So you have to upgrade the lot to gain much performance.
Note also graphics cards are very important in games playing. You need space in the case for a graphics card, plus the right slots, plus probably a more powerful power supply (a 350W is probably not enough).
Sounds to me like you need a complete new PC.