Okay lets summerize here. 1) DBAN is software it doesn't break 'hardware' (like your cell phone service has no way to cause your cell phone to catch fire suddenly). 2) DBAN is going to 'stress' parts of the system as it wipes the whole hard drive, so if your system is ancient (it is) you can (and did) find further hardware problems. 3) If you remove the GPU, and there still is a place to connect on the motherboard your video , that is IGP (your wording is a bit off that makes it sounds like ONLY the GPU has the ports). Having the GPU out AND the system won't start is a BIG SYSTEM ERROR. Further your indicating there is no 'BEEP', the BEEP is the BIOS part of the Mobo so it says 'that is a keyboard, that is a mouse, etc.' before it hands off to the Operating System (Windows) hey when you get this 'code' that means he is hitting the F key, or if you get this 'code' then he is right clicking, etc.
That it DOES NOT BEEP at all, is a indicator the BIOS / Mobo is toast. The ONLY check for this is MY INSTRUCTIONS TO FOLLOW. The battery still provides a 'charge' to keep the 'time' and setting, hence why I said "REMOVE THE BATTERY" after unplugging the power supply. If plugging it back in and the power (AS I SAID) doesn't work then your MOBO is DEAD.
Personally at this point, you wipes the OS, the mobo is acting up, the system is ancient, it is VERY COST EFFECTIVE to just dump it at this point and get a new PC from Walmart (nice i3 Core simple desktop (or better yet get a lappy!) with 6-8GB of RAM, 500GB-1TB Storage (HDD), Windows built in, normally comes with NEW LCD, Mouse and keyboard) all for a whopping $249!!!! If you want nice midrange a i5 with a seperate video card is only $100 more.
Black Friday is around the corner and even bigger deals will be had then or Cyber Monday. Getting parts individually would be too expensive in comparison (you have to buy new Mobo, New Cpu, new Memory all to match, then probably the power supply wouldn't be strong enough/right sockets, so there is a new case and PSU, etc.).