I have FINALLY found the solution - I don't have much time to spend on dealing with the blog but I spent several more hours working on this @#$% problem today - after having tried almost EVERYTHING (including exporting the entire blog to a different site where, of course, the same problem existed). That lead me to suspect that the problem was with WordPress and the way it interacts with Micro$soft's IE - especially since the problem never appears with other browsers.
So. . . on the test site I created two blogs - one with the backup from the problem blog and the other one was a completely new blog - both of which I installed this theme. Lo and behold, the blog with the backup data still had the problem with the right sidebar not showing up in IE but the completely new blog had no problem whatsoever.
In complete frustration, I thought I'd delete all 100+ posts from the problem blog (I had even gone into the database to see if there was something I could find there - of course, there wasn't anything I could find).When I deleted ALL of the posts, the problem blog suddenly started to work again!!! Aha! That was the clue - I guessed (correctly) that the problem could be found in one or more posts. Not knowing what else to try, I started deleting groups of posts and checking the blog. What I found was one post, that I had written more than a year ago, that was causing the problem. Just looking it; however, revealed nothing so I decided to look at the HTML behind it and THAT is where the problem was!!!! I had written a post on the blog where I had cut and pasted a news release that someone else had created - the HTML behind that code revealed it was full of Micro$soft html junk. Specifically, that code started with:
<!--[if gte mso 10]>
<mce:style><! /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} ></div>
<div mce_tmp="1"><! [endif] ></div>
and the rest of the content had a bunch of similar garbage around it. After removing the above, Athahualpa started to work properly again! In other words, M$ own garbage code essentially prevented IE from displaying WP properly!!!! In other words, Google Chrome, Firefox, etc. handles M$ garbage better than IE does!
Of course, I then manually cleaned up the rest of the code and now everything seems to be fine (except I messed up other things - widgets and custom graphics - as I've tried to fix this mess for so long).
The final question is, why did this take so long? While I don't know when this problem first started - the problem post was written a year ago, I suspect that M$ IE wasn't as cranky with older versions of WP. Perhaps this all surfaced with I upgraded WP but, as this problem has gone on for so long, that I don't remember when it first started! Just the same, if your right sidebar disappears from the home page of your WP blog but seems to work on other pages, you might want to look for a post or posts that contain M$ HTML messes in them. Getting rid of them solved my problem.
Now, I have to go back and restore all of my widgets and other custom things. . . .