Actually, no, there's been no previous case of such a behaviour.

Tell you the truth, it sounds like some other programme or setting could be interfering or causing Nexus to momentarily appear.
I'm running Win7 on a dual-monitor setup right now, with similar arrangement, and see no such behaviour.
Are you running anything else? Like, any dual-monitor extender or something?
From your brief description, it sounds like something's interfering with the window positions on alt-tab.
Or maybe it's something as simple as a display driver bug...

Actually, don't waste any more time looking for monitor drivers. They change absolutely nothing, apart from the identification string in the Device Manager.
It also stands to reason that you'll be using the nVidia drivers and that is a good thing. Just make sure they're updated and that you're not using an old version. For the record, the BIOS version you quote is *not* the driver version.

Now, as to what's causing this... you have to do some trial and error. Does it happen when no applications are running? If you terminate all programmes and just open up a few windows of Windows Explorer, does it still happen? How about when there's no external monitor connected? How about that Mirth Connect? Does it happen when that's not running? Or if you move all of its components to one monitor?
Well, I guess you get the point of what I'm trying to say. Just trying to see if we can narrow the possibilities a bit. If it's a driver issue, it should be happening in all cases. If it's a specific programme causing it, when that programme isn't running, Nexus should behave normally.

Also useful is the test you plan to do, with the monitor at home as well, even though I expect it won't make any difference.

Memory has nothing to do with it, I'm sure.

Do you have the dock displaying the currently running tasks (e.g.; like the taskbar)?

Actually, the last sentence you wrote might be of relevance:


You should completely disregard the HP drivers or anything that has to do with HP. Yes, the laptop might be constructed by HP, but the days when computer manufacturers actually designed their own hardware have long passed.
Go to the nVidia website and download the latest drivers for your GPU directly from them. Don't worry about HP "warnings", the only thing HP does is to get the very same drivers from nVidia and re-package them so that, instead of the nVidia logos, you end up seeing their own. And of course, stop updating their drivers far sooner than the actual hardware manufacturers themselves, so that you 'think' your computer is obsolete and go buy a new one.
If you have any experience, especially with laptops, you will agree with me that most manufacturers don't have drivers for the latest operating systems on their websites for a multitude of older laptops, even though the computers themselves are more than adequate to run said operating systems and despite the fact that the various component manufacturers have released updated drivers for their products, supporting said operating systems.
The "official" excuse is that either the drivers are included in the Microsoft repository (so they will be downloaded by Windows Update automatically) or that laptops that were "designed" for a specific operating system (say, Vista) do not officially "support" newer operating systems, and since these models are no longer sold, they don't bother keeping the drivers updated.

Of course, why any PC would "support" one operating system and not another -- say, Vista but not Windows 7 or 8 -- is a question only the geniuses of these manufacturers' marketing departments can answer.

I also have to say that 4GB of RAM is more than enough for most computers, unless you're running something extremely memory-hungry. It does not matter that you're running Windows 7 Enterprise. The differences with Win7 Ultimate are practically none, except the activation procedure. It doesn't mean that the "Enterprise" flavour has increased memory requirements or anything.
So, unless you're running some programme which needs large amounts of RAM, going to 8GB will change little to nothing. For the record, if you're running a 32-bit version of Windows, your operating system isn't able to access all 4GB, but (depending on the specifics) from 3.5 down to 3GB. Expanding the memory of that computer to 8GB will only mean that the unusable memory will increase from 0.5 (or 1GB) to 4.5 or 5GB. You need to install the 64-bit version of Windows 7, in order to make use of all 4 (or 8) GB of RAM.
But in any case, from what you've said, I cannot see how any of your usage scenarios would go even remotely close to 1GB.
I'm currently running Waterfox (64-bit build of Firefox) and it's using around 2GB of RAM, but I've got around 350 tabs open. Also, my mail client (Thunderbird) is using less than 200MB of RAM with 4 mailboxes open.

However... jEdit is running through Java. For the record, Java is bug-ridden and unstable, especially ever since Oracle took over. If you need an advanced programmers' text editor, I strongly suggest you find a native alternative, one that doesn't use Java. I personally use Notepad2, but there are lots of others, like Sublime Text, which is quite impressive.
I'm not saying that Java is (necessarily) guilty, but I keep as far away from it as possible.
In your tests, jEdit might be closed, but is the Java runtime still running?

I'm not claiming to be an expert, but I have a feeling the following could be the culprit.

1. DL and run Malwarebytes in Safe Mode and remove any offending malware. Don't run in it Safe Mode with Networking. If you have Malwarebytes already, make sure you update it to the latest version before going into Safe Mode. VERY IMPORTANT. If it flags a particular program/folder especially with multiple entries connected to that program, don't remove it via Malwarebytes, uninstall it using Revo Uninstaller when you boot back into Windows. Uninstall the program using the Advanced mode. When using the free version, certain aspects have to be done manually which isn't difficult.

2. Your video/graphics card could be the problem. If that's the case, there's probably not much you can do about it since it's a laptop as far upgrading. Replacing it with the same one (lot number) obviously won't change anything if in fact it's defective because of manufacturing. The company would have to acknowledge there is a defect and make a new one (lot number) available for replacement.

3. And as mentioned in the prior posts, the drivers for your video/graphics card could be the problem.

4. Your monitor could be showing signs that it's about to fail.