Dealing with HD video has two main components. The first is the ability to decode the highly compressed video (which is computationally intensive) and then is the ability to deal with the large uncompressed data (which is bandwidth intensive).
The fastest encoders/decoders use the GPU on the graphics card to improve performance as a GPU is far more capable at attacking the problems related to rendering and compression than a traditional CPU is. So if you have one of these, then the GPU is by far the most important piece. If you don't however, then the CPU becomes by far the most important piece as encoding/decoding on a CPU is very, very intensive.
As far as dealing with the uncompressed data, the relatively small compressed files will be decompressed into memory and then played out of memory, so it is important to have high speed RAM, but not necessarily the need for a lot of it for play back. For editing on the other hand, quantity becomes a bigger factor since the more video that can be stored in memory, the smoother your editing experience will be.
Finally, you have the hard drives. It is very helpful if these are quick for loading videos (particularly for editing) and also for working as scratch disk (where editing stores temporary files that don't fit in memory), however it is probably the least critical part. This can change though if you start working with higher quality, less compressed video where the file sizes start getting larger.
So, to summarize, GPU is highest priority if your software can use it, otherwise CPU and then speed of memory, quantity of memory and speed of hard drive in that order. CPU is still second most important if you do have GPU processing support. If you don't, then GPU is of almost no importance at all.