Yes your PC is crap. You need a new GPU and CPU as you've identified. I'm not sure the motherboard will support an AM3 socket CPU. BEst thing to do is go to the manufacturers website and see if they have a BIOS flash to support the Athlon IIx3 440.
Also you'll need to get some adapters for your PSU to power the GT240 GPU, since you list it as having no PCIE connectors.