i have just been advising Audeal on a similar topic... click here
the desktop that you described there is indeed not powerfull enough to edit video effectively/comfortably.
Can you buy a new desktop? or at least upgrade you current one? do you know how to upgrade the motherboard yourself?
what you need to get is dependant on your requirements. What type of editing do you want to do? is it just home video's? do you want them to be DVD's or just avi's or mpegs?
you camera has a firewire link so what you need to get for your laptop is a firewire card.
You laptop spec is fine for video editing, maybe your hard drive on it is a tad small for digital video editing, but i think it will suffice for someone just starting out on video editing.
Ideally you can pick up a desktop suitable for your need and prob more for around £500, even better if you don't need a monitor.
hope this helps.