Hoo Boy ! sounds to me like you have a whole mess o' problems....
you could try starting up in Safe mode....that does a few basic tests on startup and loads the OS with minimal extensions....
to access it on your 2014 Mac Mini, here's how to do that: (see link)
How to use safe mode on your Mac - Apple Support (CA)
I'd hazard a guess that you've tried the usual things..... reset smc/pmu and zap pram 4 times on startup...... your Mac mini does support Internet Recovery, so maybe give that a try: Hold down Option and Apple+R on the keyboard on startup...make sure an Ethernet cable is plugged into your Mac mini and that you have working Internet service....you'll know it worked if you see a spinning globe and a progress bar on the screen.... here's how to do a reset smc/pmu and pram reset (zap pram) courtesy of Apple and rkaufmann87.... see link
SMC and PRAM Reset - Apple Community
It's weird that your Mac mini works with your HD tv, but not with the built in video...... about the only thing I can tell you before I go is that HDMI is not hot-swappable. If you want to make or change a connection, both things have to be off first....
anyways, good luck to you, gary straiton.... try that reset smc/pmu and zap pram first, if that doesn't do anything, then go for safe mode, and if that's iffy, then go for either Internet Recovery or plain Recovery (Apple+R) or hold down the Option key on startup to get to the startup manager, from there you should be able to access MacOS's built in Recovery partition, and from there....maybe get somewhere.....anyways, give it a shot and feel free to post back here......
john B
