Check if your current PSU is able to deliver at least 2 amps of current from the +5VSB terminal, the psu should have some specs of the current delivered by its outputs. This voltage and current is delivered to the motherboard even if it's turned off in order to keep the main circuitry ready to boot up, basically.
And yeah, you might need a brand new PSU.
And yeah, you might need a brand new PSU.