Nick,
The older laptops with an RS232 port will probably still be running on Vista and beginning to show their age.
IMHO a better solution would be to look for a good XPsp3, or Win7 machine and buy a "good" USB to Serial bi-directional adaptor. I use Keyspan adaptors on all my machines - no issues, no drama.
I heard bad reports on Serial-USB converters... find it more attractive not to deal with the extra complexity. On the other-hand a faster newer machine should be easier to cope with the camera for guiding etc.
I think your laptop can meet all your needs...
BUT if you're working "remotely" and the laptop is outside... it may be safer to work with two and accept that the outside machine may get more punishment!
I use an ol' ACER i3 win7 outside for the telescope control (AstroPlanner/ CdC/ EQmod) and image acquisition (AstroArtV5/ PHD2) etc. and Teamviewer to link to a similar spec'd machine in the office for subsequent image processing (AstroArt/ BASS Project).
Hope this helps.