Hello.
Your case needs clarification.
Are you using direct Internet access, or via local proxy?
What DNS server are you using to resolve internet names?
Have you tried to ping a couple of external addresses (by FQDN) during the issue?
Have you tried to open any external web-page using ip-address (not FQDN) during the issue?
Try to logon to ASA and check service-policy[s] to see if it's blocking new connections.