Hmm ... check the specs below and compare them to your own specs. I really cant think of why it wont work on your laptop if you can run it on your other system which has less Ram.
Sony Vegas Pro 8 System Requirements:
* Microsoft Windows XP SP2 or Windows Vista
* 1 GHz processor (2.8 GHz recommended for HDV)
* 200 MB hard-disk space for program installation
600 MB hard-disk space for optional Sony Sound Series Loops & Samples reference library installation
* 1 GB RAM
* OHCI-compatible i.LINK® connector/IEEE-1394DV card (for DV and HDV capture and print-to-tape)
* Windows-compatible sound card
* DVD-ROM drive (for installation from a DVD only)
* Supported CD-recordable drive (for CD burning only)
* Supported DVD-recordable drive (for DVD burning only)
* Supported Blu-ray recordable drive (for Blu-ray burning only)
* Microsoft .NET Framework 3.0
* QuickTime 7.1.6 or later