Maybe check the manual for the keyboard and mouse to see what the blinking might mean.
Anyway..
You can try unplugging everything from the in between the PSU and the I/O switch on the case and replugging it. or go further and unplug absolutely everything and replugging.
You can also go straight to the assumption that something's wrong with the hardware (EDIT: cross-out Don't plug anything into the motherboard for this you just want to hear beeps right now.). The most definite way would be if you have an different working PC:
For the switch:
Plug the new cases switch into the old motherboard.
For the PSU:
Use the new PSU in the old PC in place of the old PSU.
For the Motherboard:
Connect the new motherboard to the old PSU and...