First, check http://status.secondlifegrid.net/ to see the current status of Second Life. Assuming your friends are logging in, it's likely the problem is on your end but you mentioned issues with specific sims. Have you tried logging into different simulator regions? For example, trying setting your start region to Ahern, Carnapt, or some other region name you know. To do that, you need to set your viewer preferences to show the start location on login (Me, Preferences, check 'show on login') and than select "type in region name" from the 'start at' box next to the login information.
Assuming that doesn't work, it's remotely possible that you've changed your firewall settings and have somehow blocked SL logins - not likely but check your security software.
You may have accidently enabled logging into a different grid besides the main Second Life Grid known as Agni. If you see a grid name box below the 'start at' box, make sure the name selected is Agni and not some other grid name.
Try to uninstall and reinstall Second Life. Google 'uninstall reinstall second life' and select the first result which is an old Second Life wiki instruction on how to do it.
All that doesn't work and it's probably an account problem and you will have to submit a support ticket - see:
https://support.secondlife.com/create-case/
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