The only time you don't need a separate GPU Card installed is if you have a APU (Processor with Integrated Graphics) installed. Thus you can use your Motherboard's Video Outputs to your monitor.
But if you have a regular CPU Processor you will need to install a separate GPU card to get video output to your monitor.
You can use your old GPU card as long as you have the proper PSU and PCIe Slots on your motherboard.