Then lets look at this logically. If you say that some usb flash is correct and it should boot. If you say that the bios is correctly set to allow it to boot then it should boot. Somewhere in this is not true because it is not booting.

That is correct, everything is set to boot and seemingly it should boot, but it doesn't Hence why I came here looking for help with diagnosing the problem. I have no clue what else the issues could be arising from. It seems to only boot certain things, regardless of the type of iso (hybrid, etc) I copied to the drive (with dd) or the method of configuration (refer to above mention of gparted live usb setup).

I tried a test while I was troubleshooting things on my own before this post with the same debian 7.5 netinst image. I used dd to put the image on flashdrive-A (1gb drive). When done from my desktop, any attempt to boot the drive was fruitless, was never recognized as even being connected. When the same procedure with the same image was done from my laptop (dd the deb 7.5 netinst iamge to drive-A), and attempting to boot the drive on my desktop it worked flawlessly. Had the same results with a linux mint 17 image on a 16gb drive.

Conclusion of the above, I was able to get a debian liveusb to boot, but only when it was created on my laptop. Which leads me to think that for whatever reason my desktop doesn't allow the system to write a drive properly.

Now this leads to the question, why could this be happening, what could be causing this problem? It cannot be the OS on the desktop in which I create the liveusb, as I have tried it now from my previous debian install, and linux mint, and as mentioned the drive failed to be recognized when boot was attempted.

Then let's start the issue with that. Can't create a live usb from desktop.

Ideas may be usb controller off or going bad/voltage issue/data issue.
Issue between controller and usb controller as in speeds or such.
USB 3 issue.
Ram so test for a day or so with memtest. Start this test.
Hard drive not able to supply proper data, cpu issue, or other data path issues. Test iso md5 on disk, the copy the iso as a file to the usb. Is the md5 the same? (shal will work also)

If your test varied only by source of the system making then we have to focus on that. We can't go off and assume pae or 64/32 bit.

MD5 checks are always correct, and both my systems are using the same arch and kernel. So definitely hardware issue.

I'll fire up a live disc and run memtest tonight. Does it generate a report at the end of testing cycle for what passed, what failed, what needs checking, etc? I have never run a test all the way through before.

Did you do that test as I suggested? Move an iso or other large image back and forth between usb and internal drive a few times. Then test md5.

Not yet. Had some other things to take care of. Will update tonight after memtest is complete.

When you say "Move an iso ... back and for between usb and internal drive a few times" do you just mean copy it back and forth, or dd?

Just copy large file back and forth and test on both ends.