Hello, Sorry to hear that. I also would like to apologize for my late reply I was busy yesterday.
Well, you say the peripherals turn on and off during boot but the system stays on. If it was a HDD error I don't think that it would do that. Could you take a video of the process? And upload it to YouTube unlisted. And either post it here or PM it to me. Could you also include a view of the setup/bios and the f11 boot menu with the HDD, USB and DVD inside.
I think that it is more likely to be the motherboard than the HDD but you may test another HDD if you have one available. I know that you can get a cheapy no brand1TB for $35 on amazon 500GB or lower should be even cheaper. But I highly doubt it is the drive.
Could it be the PSU failing to supply power properly? I highly doubt it, but for the sake of ruling out all components could you please include a detailed list of all your parts. (i.e: look at my signature)
If possible can you include pictures of the setup and wiring? Or include it on the video? (If you are unable to take a video can you take photos, lots of photos, include all error codes if any and detail all beeps if any are given by the pc, make sure the pc isn't set to "fast boot" in the bios/setup. (Also how comfortable would you say you are navigating the bios? On a scale of 1-10, is this a prebuilt [if yes what model] or a self build? [if yes is it your first time?))
A simple way to test the drive is, does it show up and work on another pc? You said you ran DBAN on it I am assuming you did so on another PC. If so then the drive is likely working.
Does the PC also fail to boot from the DVD?
Could you detail the process in which you attempt the install?
Are you 100% certain you are booting from the DVD?
You says you get boot loops no matter what? What happens if you turn on the PC with no HDD
Just the main board, CPU, Ram, mouse, keyboard, and Monitor.
What happens if you do the same and turn it on with the DVD inside?
Have you tested the RAM?
Last resort... Have you attempted to contact a professional in your area? If you're tight on money you could go to a local college and see if a computer science major is willing to take a look at your pc.