Right click on your "My Computer" icon and it will tell you your: operating system, processor type and speed, amount of RAM you have installed.
To check your video card specifications and type go to Hardware tab after doing the above, then click on Device Manager button and once there scroll to where it lists Display Adapters - the name and type of video card will be there and you can look it up on Google.
OR
Download and install Everest Home version from
here and run it and it will give you all the above information and more about your computer - expand the Computer icon on left side, then click on Summary.
Most video editing software requires at least 1GB RAM and a reasonably fast processor - very minimum would be 3.2GHz pentium 4 and even that would be extremely slow to render video files. A decent video card is also a good idea to help speed things up.
Neither of the programs mentioned above are particularly good at editing video - are you meaning to edit or just compile video files for burning to DVD?
I know you have purchased Roxio and are trialling Nero - neither give you too much more than you already have with Windows MovieMaker (installed on all PC's with Windows)
If you intend doing much video editing check these out - yes, I know you don't want to spend more money but you can download fully functional trial versions which will at least show you what is available for not too much money.
Adobe Premiere Elements 7
Sony Vegas Movie Studio 9 Platinum
Both of these offer multiple tracks of audio and video allowing layering and Picture in Picture, green screening and many effects and transitions.
Both allow you to burn to DVD directly and Premiere also allows for direct upload to Youtube
Hope this helps