Note: I am not asking how to limit asking to a site by means of a static IP address, this is already done in my .htaccess file. I have a particular site I will need to access on the road often but will only be doing so from a particular machine.
In short, is it possible to limit access to a particular website based on something specific within a pc other than IP?
Set up SSL on the web server and authenticate to it using a certificate that only exists on that particular machine.
Have a look at this article for an introduction.