Safari no longer connects to the internet

Question

I upgraded to OS Yosemite in my iMac (must be approaching 4 years old) and everything has been working fine.  Had a couple of applications where they closed unexpectedly, but nothing major and things have continued as they always have.  Apps have also automatically updated.   As of today, Safari will no longer connect to the internet and I keep getting the classic "the server unexpectedly dropped the connection" blurb and I kept being told that a disk that I hadn't put in the machine is not being recognized.
I'm typing this on my MacBook Air so I know that Safari can work fine (also having no problem with my iPad or iPhone) and there is no issue with my ISP' modem (I'm with Virgin Media), connector or Netgear wireless router.  Tonight I have performed a recovery install and now I have this annoying message saying how I need a particular Java plugin, which I can't sort out because Safari can't connect to the internet.  I have also performed a router reset, without remedy.
Logically, as I see it, the issue lies with Safari, and due to it being the only internet access on my iMac, I can't even download Firefox or access the App Store so looks like I can't update.  A friend is also having the same issues with his iPad, so I know this isn't just my iMac
Looking for some answers here?  Anyone?
Thanks

Answer 1

Please read this whole message before doing anything.
This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it.
Step 1
The purpose of this step is to determine whether the problem is localized to your user account.
Enable guest logins* and log in as Guest. Don't use the Safari-only “Guest User” login created by “Find My Mac.”
While logged in as Guest, you won’t have access to any of your documents or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this behavior; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
Test while logged in as Guest. Same problem?
After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
*Note: If you’ve activated “Find My Mac” or FileVault, then you can’t enable the Guest account. The “Guest User” login created by “Find My Mac” is not the same. Create a new account in which to test, and delete it, including its home folder, after testing.
Step 2
The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.
Please take this step regardless of the results of Step 1.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem. You must hold down the shift key twice: once when you turn on the computer, and again when you log in.
Note: If FileVault is enabled in OS X 10.9 or earlier, or if a firmware password is set, or if the startup volume is a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to start up and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal startup may also be somewhat slow.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem?
After testing, restart as usual (not in safe mode) and verify that you still have the problem. Post the results of Steps 1 and 2.