Gosh, and I was about to say that programs will open on the last display on which they were closed.
Almost always happens this way, if the program is written to standard Windows-conformant API. There certainly are exceptions, like non-standard or custom-built programs with custom-GUI that say always open on monitor 1 (say, in full-screen), even if you drag them over to monitor 2 and put them in "window mode" before closing them. They will simply always open on monitor 1 in full-screen when launched no matter where they were when last closed, because that's how the author wrote it.
Nevertheless, back to OP... I think OP's wording in his problem description may have confused me when I responded earlier:
yet when I open a new program (whether it is a game, browser, or media player) it changes back to the old over/under set up.
I think when he said "when I open a new program" I thought he was talking about a "newly, freshly installed brand new program run for the first time". And so I couldn't imagine how that first-time brand new open could ever be anywhere but on monitor 1.
But now that I see your comment, and look back on his words, I think his "open a new program" may really be describing "re-launch a new instance of a program that was closed previously". And now I see the applicability of your comment, since almost certainly a game, browser, or media player are ALL Windows-API conforming, and as you point out there's near 100% certainty that when re-launched they would once again re-open on exactly the same monitor and at the same place and with the same window size as when last closed.
This has happened to all of us who've had 2-monitor setups and gone to a 1-monitor setup, or maybe swapped 1 and 2 horizontally, or in his case gone from 2-over-1 to 1-to-the-left-of-2, etc. As you've pointed out, and as OP would have eventually learned from others if he'd only stuck it out here, it's that prior last-closed state for programs you may not have used for a while but previously were on the now "phantom monitor location" which actually no longer exists, which is almost certainly the explanation for his problem now that his two monitors have been physically rearranged with corresponding re-specification of monitor arrangement using the video driver Control Panel (or ATI's CCC, etc.).
And, the solution (for him) is easy... even if you have to go through it for each program as you first come to it again from its wrong opening on the "phantom monitor old location", as clearly explained by Brink in his "tutorial" for exactly this problem and its resolution:
Check
this tutorial for the easy way to drag an off-screen window back onto your primary monitor.
Anyway, the above tutorial is just a few steps, and allows you to right-click on the Aero preview window and select MOVE, and then use your arrow keys on the keyboard to slide the actual window over from off-screen (invisible) onto your true primary monitor.
Hope he's following "silently".