How to do sites uniquely identify a computer/network online?

Ways to uniquely identify a computer remotely apart from IP address (or MAC, which isn't possible):

• HTTP cookies
• HTTP DOM storage
• If you have an HTTP proxy such as Squid, sometimes these proxies can pass your private IP in a Via: HTTP header
• A Java applet or Internet Explorer ActiveX control can get many of your system details. You'd have to have allowed the plugin to run previously.
• I have a faint memory of reading something about a way via Javascript that determines the fonts on your system, possibly causes another one to be installed, and checks for that font.
• Flash cookies
• Adobe's Flash engine may also have access to many system details.
• Other browser plugins or extensions can cause your system to reveal information about itself to the system you're trying to connect to.

One possibility is your ISP. Your network's IP address may be being mapped to an ISP's address before being passed to the surveyor's servers. If this is the case then if the lease on the mapped IP address hasn't expired, changing your local network's address won't have any effect. The ISP will still see your local network as connecting on a specific ADSL line.

Not all ISPs do this and where it is done it is to try to re-use IPv4 addresses within the ISP's customer base.

(...and do you really need to do a survey more than once a day - against their rules?)

They are most likely doing checks for BOTH IP address AND A cookie (or some other characteristic served up by your browser). As stated by someone else, it is almost impossible for them to be using your MAC address - for 2 reasons - 1 - Your MAC address would change when you change computer and 2, your MAC address is not broadcast onto the Internet.

It might also be that when you changed your IP address you were changing an Internal IP address behind your router, and the router rewrote it to its external one - this is common practice. If your IP address started 10. something, 192.168.something or 172.[16-31].something this is most likely what happened.