If I had your situation on MY computer, I would not be looking at a complete reload of Windows, along with all applications and data.
 
I am also not at all sure about the concept of loading a Windows image from one computer to another, due to chip set and other driver issues, registry issues, and application issues.
The only time I have ever seen something like that is ghosting identical machines from a master copy, where identical hardware is present between the computers.
 
 
I do not believe it would work at all, and in any case, it is certainly not needed for your situation.  Simply completing the removal steps for the failed X3 install would be the only software task to finish prior to installing it again.  I would start with that.
 
If your computer is that old, I would suggest you complete the X3 trace removal, then install it again, and see if it works on the older computer.  If so, then you are OK for a bit, while you contemplate upgrading to a new computer, at which time you could install X3 on the new computer - allowable per the Cakewalk software licence agreement terms.
 
Doing things per as noted above gives you a free shot at seeing if it will work with the computer you have.  I DO recommend you consider picking up a new computer for X3, as it will make a HUGE performance difference, and may well be more stable as well.  
 
There are a zillion thoughts from a zillion folks on what specs would work for a computer to run Sonar on.  There are purpose-built computers available for running Sonar, as well as fully functional Best Buy types of pre-built computers, or you could build your own.
 
I would suggest an Intel-based i7 processor, on a good motherboard, with 16-32 GB of memory, a solid-state primary hard drive, one or two regular 7,200 rpm SATA III drives, and either two or perhaps three displays.  I use the on-board graphics of my computer and do not have a separate installed video card, and run two displays just fine.  You could always start with that and then decide if you wanted to pick up a more robust video card.  For displays, I chose to use a 32" HDTV ($200), and a 46" HDTV ($354), and those work wonderfully well for me.
 
If picking up a new computer, make sure drivers exist for any hardware you have, such as for a dedicated audio interface, for the version of Windows you would get with the new computer.  Please note that I have seen several reports on the web of Windows 8.1 driver issues.  I happen to use Windows 8, and may or may not ever upgrade it to Windows 8.1 - I happen to really like Windows 8.  Windows 7 is also a fabulous OS for running Sonar.
 
Bob Bone
 

overdubI can always use X2 until I have the time and energy to revisit X3 on the DAW.

Good plan; keep going as long as you can.

overdubI haven't yet run the MD5 app so there's still a chance the download could have a glitch.

Absolutely. Best to make sure of those first. Least work involved.

overdubThe prospect of reformatting and re-installing Win 7 on this machine is time consuming enough but having to back up 500 gigs and replacing it all again makes belly and my head hurt.

Although it's possible these days to keep everything on one hard drive, even with a DAW, having a second drive for projects makes it far easier in a situation like this. However, with that said, you're doing periodic back-ups anyway, right? We all do, right..? Yeah, we do... riiiiggghhtt.

overdubOn the other hand, I haven't tried any modern backup programs, and I am rather fond of a clean OS.  So, who knows, maybe I'll wind up going that route.

That AOMEI app is relatively fast. Mind you, I don't remember what my times were on older machines or if I even used it back then; I've been through several back-up apps over the last (OMG) 28 years banging on computers.

overdubIs it feasible to use the image of that system on top of a new MOBO?

It can be done, but I don't recommend it. There are a lot of devices built into motherboards these days and every one of them needs a driver installed. Unless you buy the same brand of motherboard and they still outsource devices to the same third-party companies and those third-parties still use the same or comparable drivers, you might not have a lot of massaging to do to get everything working well. On the other hand, Mr. Murphy had a few things to say about how well things go when you think there are no unknown factors. I'm not trying to scare you; I'm just saying until you've got some experience with building a few PCs from scratch, resourcing parts, etc. it's best not to get involved with swapping motherboards under those conditions.
 
Hope this helps.
-Ron T.
 
PS: You'll likely want to switch to a 64-bit mb anyway; I doubt your current one is unless it was very high end when you bought it (considering the age and all).

"Shift click and Select the 4 Sonar install files.
Right click and select extract here.
Windows will create one setup.exe file and about 10 or 12 or so .bin files (I forget the exact number)
Then just double click the setup.exe file and away you go. I've found when people have installation problems this is often the easiest fix if the installers aren't corrupted."

Well, Mike, after countless hours of agonizing over my installation woes, your suggestion quoted above actually forced X3 to install on my DAW! Thank you very much!!
It wasn't totally smooth sailing, mind you. There were several hundred files, mostly Session Drummer sounds and perhaps some loops and such, that stopped the installation along the way and I had to click 'ignore' about 500 or so times...really... but I was determined to get all the way thru setup even if I had to click 'retry' for another hour or two. It worked!
I've run X3 and put it through a few paces...nothing extensive yet...but at least it's mostly installed and seems to run just fine.
I can't help but wonder if those missing files (during setup) were part of the extra 'loops and one-shots' installation folders that I left out intentionally? I had read that I only needed to install the four, basic, X3 installation folders, so those were the only ones I extracted 'here' as you described. I had the previous 'X' versions installed and was under the impression that all of the extra files were the same as those on X3 and therefore weren't needed since they were already in place. Someone, please advise if I'm wrong about that.
In any event, since setup completed, it shouldn't be a problem adding what's missing, if that's the case...or even uninstalling and re-installing more completely if necessary wouldn't be a problem since your technique seems to work magic.
On the other hand, if those missing files were supposed to be in the folders that I installed, there must be something corrupt somewhere. The HASH numbers all matched the originals so they're not the culprit.
But if I'm only missing Session Drummer sounds and maybe a few others, I don't really care about that. I'll be using Addictive or Superior Drummer anyway.
Again, thanks for everyone's help, and a big thumbs up to you, Mike. You saved the day and more.
Dub