Google Chrome has recently had an issue with youtube (go figure) where, upon closing the youtube tab, the browser would crash. I don't think that is your problem, but it's worth noting.
It could possibly be a memory issue, try looking Microsoft's memory diagnosis tool, it will tell you if there are any bad connections in your RAM cards.
Another thing to check is to run an antivirus scan. There's a chance that a virus could be interfering with your network connections. I suggest Microsoft Security Essentials (a lot of people put trust in Avast or AVG, but if you look at the facts, MSE is the top anti virus right now, and it's worth the try).
Make sure all the browsers are at the latest STABLE version. I know both Firefox and Chrome have developer builds that you can get, and I'm assuming Opera has them too. If you use a developer build on any of these, try reverting to the latest stable build, there's a chance that a developer released a patch that he/she didn't test properly.
Lastly, do some trouble shooting online. You can usually assume that, if it's not your hardware, others are having the same problem. Google is the greatest tool for the internet ever produced and will definitely help, if not fix, your problem.
Hope I helped!