|The info you provided is only semi-useful. We need to know the make/model of the motherboard, the type of RAM (DDR or DDR2), the speed the RAM runs at, whether your video card is AGP or PCI-e.|
"Processor: Intel(R) Pentium(R) 4 CPU 3.40GHz (2 CPUs)"
If it's a P4, it's a single core CPU. If it's "2 CPUs", you either have a dual core Pentium D or a board that physically supports two separate CPUs. Assuming it's a Pentium D, it's most likely a D945 or D950.
The 7800GT was a high performance card about 4-5 yrs ago...now it's roughly equal to a low end 9500GT, but without the latest pixel shader or DX10 support.
For gaming, you'll definitely need to upgrade the video card. Can't advise you on the CPU without knowing which board you have.