Advice on sluggish Safari please

I'm using an iMac with Snow Leopard and Safari 5.12 and having increasing difficulty visiting most websites. I click on the bookmark and the wheel spins for ages until I get "Safari Cannot Find The Server".

However, my partner is using a MacBook Air, also with Snow Leopard and Safari and she is using the same BT Broadband wifi connection as me and has no connection issues at all - it's quite fast.

So I think I have to assume the problem is in my own computer, and not the connection.

Any ideas where to start, please?

It's getting such that even my home page frequently doesn't appear, and it's lucky that I am able to post this.

Any help welcome please.

Regards, Mike

Edit: P.S. Forgot to mention that I also have Google Chrome as a browser, but it makes no difference, I get a large notice saying "This webpage is not available". It says the DNS Lookup failed.