Over the last week, I have been vacationing in Seattle and the place that I am staying at has a very "flakey" Internet connection. There are times where I have problems connecting with my Moodle, yet, I can sometimes connect to other sites. Of course, this is very disturbing. Even moodle.org is real flakey, not just my own moodle.
Have you tried accessing your Moodle from another ISP? Is moodle.org responsive?
I rebooted my VPS thinking that it was my server, and it seemed to help a little. But I found that my best solution was to work from the local library.
Maybe you need to restart your router? I know this sounds strange, but I thought I would offer my 2 cents.