Mac Mini (late 2014) MAJOR ISSUES

Deductive reasoning has failed. In most cases - but not all - the lack of any chime after NVRAM/PRAM reset speaks to the fact the Mac is not completing the POST (power-on self-test). Most of the time this means the logic board has failed, and is not a graphics card / display problem. Without seeing / testing the Mini, this is what is most likely with the information you have provided.

A small percentage of logic boards die from 'natural causes' - e.g. manufacturing defects - but usually instead of jumping in the abyss, most logic boards are pushed. Which is to say, most logic boards are 'murdered'.

Some external force - usually electrical - acts upon the logic board and forces the demise. It could be static electricity from not having a proper static-free workstation set up when one disassembles the Mac. It could be a static shock from touching a component without being properly grounded. It could be a spike in voltage coming into the Mac from the mains. The causes are varied, but all of them are overwhelming to a logic board / processor that can't withstand most 1.5v overages. Hit it with 10K volts of static, and well... it's like the proverbial swatting flies with atom bombs.

Can you boot from your backup (if it is a clone) or from your recovery partition? I would suspect HD failure as more likely than graphics failure.

How do you know if it’s booting if you can’t see anything on the screen?

Check your RAM to be sure they are seated. Startup will fail if the RAM does not pass pre check. Could be bad.