So thanks for trying to help. Though I will provide more information for those hosting on GoDaddy.
1) GoDaddy will work with customers directly. Their general help website remains the only authoritative place to get information on what to do. I notice that Jeremy did not reference an official GoDaddy response, and therefore that type of advice needs to be verified with GoDaddy before taking any action. GoDaddy has been hosting for many years, and the various advice circulated outside their website, including on wordpress.org, may or may not represent current practice.
2) I am independently working with GoDaddy on an open ticket to resolve this issue. They have looked at my specific account from the inside, and recommended tips to try other than Linux hosting. I will not detail what those steps are since they may or may not represent what other people should do.
3) In my case I will NOT be moving marktab.net to Linux hosting. This acount also hosts dotnetnuke, which is Windows only. Note how you could get into trouble by coming to forums like this where people giving you advice start listing steps to transfer your account to another operating system without considering (or even asking for) the full scope of information. An alternative I therefore have is to find (possibly) another Windows host.
However, I am not done with my debugging tests. I wanted to see what Jeremy, representing Jetpack, would be able to offer. I have more tests to run based on the information I have from the "Core Control" plug-in, which provides advanced information on how plug-ins work with the server. Two obvious tests include whether other plug-ins which have similar connectivity profiles also experience issues. Also, I intend to stand up a new instance of WordPress and see whether that one will similarly have issues with Jetpack.
Jetpack used to work. Also, I noticed that in a recent upgrade of the same software on Linux (this past week) that I was receiving the same message. But that Linux installation was not GoDaddy, but Bluehost. I resolved that error, which was related to the max upload size parameter being set too low. At present the Jetpack zipped installation comes in at over 4 MB.
Finally, I want to give this general question to those having similar problems: ask yourself whether switching operating systems is really worth the value of a single plug-in. Or, would you be better off by finding an alternative plug-in?