How do I overcome server connection re-sets and "No Data" warnings?

I'm having great difficulty editing pages in the WP site at http://www.isi-companies.com/installation/ due to re-set server connections or, as Chrome puts it, "No Data." These do not appear to be server timeouts. They occur much more rapidly, often instantaneously. As a result: (1) I am often unable to save page updates; (2) clicking View Page or Preview Changes produces a server connection re-set message; and (3) clicking View Page or Edit Page frequently causes the WP login screen to appear instead of the desired web page or editing screen.

After having me do a Trace Route on my Mac, Tech Support at GoDaddy (the web host) analyzed it as being a problem with poor connection through the Internet and said there's nothing they can do. They advised talking with my ISP, which I did.

After considering the Trace Route results I provided and having me reboot my modem, Tech Support at the ISP said there was nothing they could do either.

The problem exists regardless of browser; I tried Safari, Firefox and Chrome, in each case clearing the caches.

Is there something internal to WordPress that can go wrong and produce these kinds of issues? (I'm using WP 3.5.2 with Dottoro Child theme and Jetpack 2.3.1.) Should I try reinstalling WP 3.5.2? Should I be looking for the possibility of malware infection or some other atrocity?

FYI, I administer another site running WP 3.5.2 with Dottoro Child theme and Jetpack 2.3.1. These issues have not occurred there.

Need assistance. I'm getting further behind every day.

ADDITIONAL COMMENT 1: I can see my Media Library by going to directly from the dashboard. Cannot see it when I click Add Media or attempt to use the Dottoro theme's Background and Pagination Image feature. Maybe related to the issues described above?

ADDITIONAL COMMENT 2: I'm trying to edit a page. When I click Preview Changes and it fails, the URL of the resulting screen is http://isi-companies.com/installation/wp-admin/post.php. When I clicked Update, the URL of the resulting screen is http://isi-companies.com/installation/wp-admin/post.php?t=1373494507088 and there is absolutely no visible content. Maybe relevant?