The only things I can think of:
- Check the rating of your power supply, is it sufficiently powerful to run everything you've got hooked up to it?
- As most of your stuff is new, you shouldn't be getting failures there but there may still be a component that failed straight out of the box of course. I would disconnect anything that's old, try to get it running on the new stuff first and see if that works without these issues turning up. Create a bootable USB with Linux on it or something like that and run from that so that you can avoid the old HDD. See if you can use a keyboard/mouse with wires to avoid connection issues there.
Others may well have better advice...
Edited to add: how stable is your power supply from the outlet? If the input power is wonky, you may get strange effects although a computer PSU may be able to deal with some variations.