All ATX boards had the 4 pin.
New boards have 8 pin but that is only required for quad core.
That board also requires 24 pin main and not 20 as some older PSU's might have.
Otherwise I suppose it will work. Again depends on voltage@amps requirements as well.
No harm in trying.
In browsing the details from Newegg most new PSU's will say "Dual Core" "ready" if in fact they are.
Newegg.com - ATX12V, Power Supplies, Power Supplies, Computer Hardware
Do you know the make and model of the old PSU?
Also note that the RAM must be 240 pin and not 184.