Well, since dealing with heavy loads on servers is part of my job, and with PHP and Apache, which is actually running this site (I think), I could give you my own thoughts. There are a couple of other techies here(and Rich) and I'm sure they told you the same... First of all, it has nothing to do with the Egypt line or whatever, it's definitely the server. You wouldnt reach the 'Internal server error' if you werent reaching the site becausde of a cut cable

This isnt a database problem either, because you would probably get the famous 'Mysql couldnt connect' error, which happens when the traffic you have on your website is higher than what your database server can provide.
This is in fact an Apache web server error, which means the site seems to be too demanding for the web server. This can happen when the webserver is getting many requests (loading a page) and each request requires the web server to execute PHP scripts, which uses memory and CPU. Since the site is on a shared server, it's probably overloading. (I don't see how having 20 tabs at the same time can be worse than reloading the same page 20 times, the memory usage is going to be on YOUR computer for using too much memory because of many browser tabs, not on the web server).
What is suspicious is that instead of getting a clear message, you're getting 'Internal error'. It might be because the web server is actually running out of memory. If you were on a dedicated server, the server could be tweaked and optimized to run the site, but when you're sharing, you can't.
My own suggestion would be to shop for a dedicated server somewhere, if you can afford, or look at godaddy.com and try to see if what's the best accounts they offer. There are a couple of bad things about godaddy.com, but they might be worth a try because they're usually very cheap and configured properly.