That error message could have a number of causes. Is it just the Runescape client not working or other websites/services too? Did you recently update your antivirus software?
If a lot of other websites aren't working as well, it's probably a DNS issue. In that case your ISP's default DNS servers could be poorly configured and perhaps caching old records. If the game servers had all changed IP lately or something, but it would be affecting a lot of people if so, namely anyone using that DNS. In any case, if it's a DNS issue, you could try using Google's DNS servers:
1. Open start and search "Network connections"
2. Right-click your local area connection and select properties
3. Click on internet protocol version 4 (TCP/IPv4) and select properties
4. Click on "Use the following DNS server addresses":
Preferred DNS server: 8.8.8.8 and alternate DNS server: 8.8.4.4
5. Save the changes
Some AV softwares are known to block RS. Avast for example. You could try adding *.runescape.com/* (with the stars) to its exclusion list or disabling the AV altogether while trying to load the client.