What are you doing when you notice it running slowly? First thing that jumps out at me is the RAM. 8GB is steadily becoming a new standard for smooth multitasking so I'd put that in for sure.
Could very well be a software problem -- too much malware / your disk is full / too many background jobs / ... I'd start by inspecting your system, before buying new hardware.
I see absolutely no reason why an "old" (!!) 2.33Ghz C2D computer with 3GB of RAM should be "too slow" after boot. Or for any common use for that matter, except perhaps hardcore gaming or scientific computing.