Okay - there are two most likely reasons why BL07 won't work for you online. They are:
1) Your Router
2) Your Software Firewall
I'll take you through these as step by step as I can - I'm aiming it a user with not much computer experience so apologies if it states the obvious to you at points.
1) The Router
Routers are pretty standard kit in the home these days - it's that box which is connecting you to your broadband or cable connection. It manages the traffic coming heading in and out of your PC and, as part of this, blocks anything which it thinks is unnecessary or potential harmful.
This applies to some (not all) of the traffic sent by BL07 when playing on-line, so you need to instruct the router to let this data flow - this is done by opening three ports (11514, 11515 & 11516) for use with the UDP Protocol. (that's a particular kind of structure of data, so we're not letting every man and his dog in)
OK, first step is that we need to find out what IP Address your computer has on the network. This is reference the router uses to send traffic intended for your machine.
Go to the Start > Run and type in cmd and press enter. This will bring up command prompt. Then type in ipconfig /all - this will produce a list of your details including your IP address. Make a note of this address.
Now open up a web browser window type in that IP Address but make the last digit a 1 instead. This should take you to your router configuration - you may be asked for a username and password and this generally is admin for both by default. Have a look in your instruction manual for it if you have any problems.
The exact process of allowing the ports then depends on the make and model (model number will be written on the underside) of your router but you can get an idea by finding your router on
this page and having a look at some guides for the games listed (you can ignore the static IP malarkey - most routers by default give you a permanent IP on first connection). The process will be very similar just with different ports. I have submitted a request to the them to create a guide for BL07 but since Codemasters reference them in the readme I'd guess they've done the same already though.
For me on my Belkin F5D7633-4 I go to "Virtual Servers" under the firewall heading it brings up this page which I fill in as below, my PCs IP being 192.168.2.3:
Click Add and communication via those ports will now be directed to your PC.
2) Software Firewalls
It's a good idea to be security concious and have something extra between you and anybody with a desire to have a shifty through your data so many of you will have a software firewall installed as well. However, this firewall may also take a dislike to some of the A lot of people will be using the Windows Firewall which came in with Windows XP Service Pack 2 so I'll deal with that and Zone Alarm, which I personally use.
Windows Firewall
Go to the Firewall Controls under Start > Control Panel > Windows Firewall and got to the Exceptions Tab.
Firstly check that the game is in the list of programs and add it if it isn't - you should have been asked for this permission the first time the program tried to access the internet however.
Now go to "Add Port" and, in turn, add those three UDP Ports (11514, 11515 & 11516) here as well - the name is just a label for your reference so call them which you will recognise. This should be all that is required.
Zone Alarm
It's even simpler with Zone Alarm. Open up the menu system and go to Program Control. Find the game in the list and check that all the columns alongside it, including the server access, are ticked (right click on them and choose allow).
See - nothing too complicated.

If you try the above and run in to difficulties please get in contact with me and, equally, if you have any pearls of wisdom to offer then feel free to add them.