|Typically, a video card with hardware-based H.264 decoding would allow you to watch 1080p video even with a creaky old processor.|
However, the Dimension 2400 only has PCI slots. PCI video cards with H.264 decoders are available, but the limited bandwidth of PCI (especially upstream) might really hurt performance of the video decoder.
A processor upgrade may give you better results, especially if the current CPU is a Celeron. The 2400 supports P4s up to 3.06GHz. The hyper-threaded 3.06GHz P4 would be able to handle 720p HD, but not 1080p.
HTPC | Pentium M @ 2.82GHz, 2MB L2) | 4GB | 1.0TB | Radeon HD5750
Blu-Ray | Win7 Pro | HDMI out to Onkyo TX-SR707