T3610 and GTX970 (possible GPU problem).

I'm not sure, if my GPU is not working properly, or maybe there is another reason... but, let me tell you my story.

I have quite old computer based on i5-5470, and I had a problem as some more demanding application caused switching off computer. I was suspecting either GPU or PSU. I was changed (literally downgraded GPU for GTX1650 - as it was less power demanding) and this computer working properly - sometimes, when I'm working long time, switching if and want to turn back on, is not starting and have to wait up to 30 minutes, sometimes even longer and eventually it starts.

As I had a limited budget, I decided to buy T3610. I installed my old GTX970 inside. But... sometimes, this PC is not starting properly - it looks like W10 is starting, keyboard and mouse are activated, but there is no signal on my display.

Sometimes I need to switch it off once, twice and starts. Sometimes, I'm checking if cables are connected properly and trying to push a bit. Couple times it has happened after accessing BIOS and exiting it without making any changes.

My PSU is 685W.

I still have nVidia Quadro K2000 - but I would prefer to have a better card, suiting my needs. 

I want to mention, when PC starts (with GTX970) working fine, no matter how many hours I want and doing a good job. Not a single crash.

What could be possible problem?