Unfortunately, many of the current games require fairly high performance systems with multi-core processors and lots of RAM, as well as benefitting from dedicated video boards which were rarely included in systems like yours.
I've run into the Dell Dimension 2400 series in several businesses and they usually perform OK with general business applications, though the disk subsystem seems to be a bit slow resulting in quite a performance drop if the PC also lacks RAM and begins to swap. This could have a drastic effect on some of the newer games which also have large numbers of images stored on disk.
If your PC has a small amount of RAM, your gaming might really benefit from increasing its capacity, generally far more than upgrading the processor which is also usually much more expensive. Adding a second hard drive with larger capacity and better performance might also help, though this is generally more expensive. Placing the Windows swap file on a new additional drive as well as installing some of the larger games there can help these more disk intensive applications.
If you've got the money, buying an entirely new PC is a better choice, but if the money's a bit tighter and you need to get more life from an otherwise good old PC, try the RAM first and then the disk, especially if disk capacity is a bit tight. A new video card is probably the least effective upgrade to most older systems since unless the video card is very high performance, it will actually require more processor and potentially RAM to support the higher resolution screens it will provide.
Bitman