Your PC connects to a DNS server which is like a telephone book. When you type in an address like mumsnet or the bbc it looks it up on the DNS server to find out what IP that is so you can connect. Right now that is not working properly.
If you have a router/modem then reboot it first and then the PC to see if that is it. That is a common cause.
If not the router I'd say it was a problem at your ISPs end, but it's been two days so I think that's out. You might want to call them though at some point in case.
Malware can do this, but then I'd expect every click to send you to a viagra site or something.
There are a few things you can try.
If you go to the Start Menu, click the Run box and type CMD (on Windows 98 you type Command instead)
Now you are in an old fashioned looking Dos window. Type ipconfig /flushdns
press enter and close the window and see if that helped.
In Control Panel open Network Connections. You should see an icon in there for your internet connection. Right click that and select select Repair.
This next one will sound long winded, but it's easier to do than describe.
Again in Control Panel open Network Connections. This time Right click the icon and select Properties.
Now you should see a box with some lines of text and the bottom one says Internet Protocal (TCP/IP)
Double click that to open up another box which near the bottom says 'obtain DNS server automatically'
Tick 'use the following DNS server addresses' and it will let you type these two iP numbers into the boxes below.
4.2.2.1
4.2.2.2
Press OK and reboot the computer. If this doesn't help then it is easy to put it back by going back and ticking 'obtain DNS server automatically'