The following checks require the computer case to be opened so take the following safety precautions 1st, disconnect the power cord from the wall socket and take anti static precautions before touching anything inside, you can do this by touching a bare metal part of the case.
Best couple of suggestions I can make would be first remove the MB and do a barebones set-up on a piece of cardboard (make sure it is larger than the MB) only connect the PSU, the GFX card, screen, 1 stick of Ram and the keyboard.
IF your MB doesn`t have a power test switch you will then need to short out the 2 power on pins on the MB header to get the PSU to activate, you can use a small flat bladed screwdriver or a paper clip bent into a U shape, this is perfectly safe if you do not touch anything else, the idea is to see if we can get a BIOS screen if you do you can then add one component at a time until you find the problem component, you must power down and remove the power cord from the wall before adding another component, second suggestion try a known working PSU, it is not unknown for new components to be bad, third suggestion try and loan an ordinary PCI graphics card (not pci-e) or VGA port again to try and get a BIOS screen.
Example of MB power pins;