l dont think its worth pursuing hotmail as MS have replaced it with Outlook mail. So there can be many reasons why you can no longer accessing it.
As for gmail, is it giving any error or something like slow access. Where are trying to access the service from, mobile phone or PC.
Try check if the gmail servers are available from where you are by pinging its IP address, the command is: ping 184.108.40.206. If you get a respond, then check your local settings.