Why not using a clients certificate inside the certificate store of an authorized host or inside a cryptographic token such as smartcard that can be plugged into any desired computer?
Update: You should take into account that uniquely identifying a computer means obtaining something that is at a relative low level, unaccessable to code embeded in an html page (Javascript, not signed applet or activeX), unless you install something in the desired computer (or executing something signed such as an applet or activeX).
One thing that is unique per computer is the MAC address of the Ethernet card, that is almost ubiquitous on every rather modern (and not so modern) computer. However that couldn't be secure enough since many cards allow changing its MAC address.
Pentium III used to have an unique serial number inside CPU, that could fit perfect for your use. The downside is that no newer CPUs come with such a thing due to privacy concerns from most users.
You could also combine many elements of the computer such as CPU id (model, speed, etc.), motherboard model, hard disk space, memory installed and so on. I think Windows XP used to gather such type of information to feed a hash to uniquely identify a computer for activation purposes.
Update 2: Hard disks also come with serial numbers that can be retrieved by software. Here is an example of how to get it for activation purposes (your case). However it will work if sb takes the HD to another computer. Nonetheless you can still combine it with more unique data from computer (such as MAC address as I said before). I would also add a unique key generated for a user and kept in a database of your own would (that could be retrieved online from a server) along with the rest to feed a hash function that identifies the system.