Adapt a computer ATX power supply to add a single 2 wire 12V connector

 I need to replace a 350W power supply that supplies a computer setup and LCD screen in an all in one computer. The failing power supply has one single 2 wire(one black, one white) connector powering a power board that supplys the power to the LCD screen.
Can I use any ATX power supply that has the same or more amps on each of the 12V 5V and 3.3V and........
Can I adapt the spare 4 pin molex connectors to make a 2 wire single connector?
I can take photos if necessary.
hi, thank you