I want to begin editing video on my laptop but unfortuantely cant afford to buy a new one so want to simply upgrade my existing machine. I would love some advice on what specs I should aim for if I wish to create 30-60minute short films on my machine using Avid Xpress or Premiere. Here are my existing specs: (from crucial.com)

Model: E-Machine M5100
Maximum Memory Capacity: 1024MB
Currently Installed Memory: 544 MB
Available Memory Slots: -2
Number of Banks: 1
Dual Channel Support: No
CPU Manufacturer: GenuineIntel
CPU Family: Mobile Intel(R) Celeron(R) CPU 2.40GHz Model 2, Stepping 9
CPU Speed: 2392 MHz
Firewire: Texas Instruments OHCI Compliant IEEE 1394 Host controller
Display: Intel 82852/82855 GM/GME Graphics controller

Questions Im interested in are.
What RAM should I aim for?
If I can, should I change my processor / CPU speed?
Will my firewire card do?
Should I get a specific video/graphics card?
Or all in all should I get a new machine?

You are really pushing it here, yes you can upgrade the ram and the HDD and get yourself an external HDD to gain extra space but the celeron isn't up to it.

Keep your laptop for the usual stuff don't bother with the upgrades, get premiere elements or avid freeDV and with the money saved get a desktop PC. They are easy and cheap to upgrade in the future and it will give the power you need for what you want to do.

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Edius Pro 4 Broadcast, Edius DVX, ADVC300 -- PremPro 2.0, Matrox RT X100

I agree, editing on a note book celron would be a trail.

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My problem is that I am in no financial situation and it may be impractical for me to buy a new desktop PC as I am living in Asia at the moment and plan to return to the UK in the next year. Therefore buying a desktop will be of little use to me as it will be too difficult to take home.

So what specs should I explicitly get on a notebook and any ideas of a general price?

core duo at any speed
at least 1gb ram
dedicated video card
as much HDD space as you can get.

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Edius Pro 4 Broadcast, Edius DVX, ADVC300 -- PremPro 2.0, Matrox RT X100