One of the most common access problems you can have with broadband is when you open Internet Explorer and you get the dreaded Page Cannot be Displayed message. This can happen for a number of reasons, but the most common cause is that your router needs rebooting. The router is normally supplied by your broadband service provider - Netopia routers with Eircom and Zyxel routers with ESAT/BT - and these are, in effect, simple computers. Like all computers (unfortunately) they sometimes hang and if they do they will not allow internet access until they are rebooted.
Rebooting simply involves turning the power switch at the back of these units off for about 15 seconds. The power can then be turned back on again and the router will start its boot sequence, which can last for up to a minute. Once it has rebooted you may find that your internet access is magically restored.
In the case of wireless routers I have come across the situation where PCs connected to the router by ethernet cable can access the internet but wirelessly connected PCs cannot. Again, while there are a number of reasons why this might occur, a quick reboot of the router often resolves the issue in less than a minute.
One word of caution, you want to reboot your router, not reset it. At the back of your router you will find a recessed reset button that can only be pressed using a pen tip or paper-clip. You should never press this button unless instructed to do so by your internet service provider (or you know how to reconfigure a router manually!) as you will clear all the configuration settings needed to connect to your broadband service.