No, USB3.0 headers use different connectors from USB2.0 headers. Scrap both the case and PSU. The PSU is old, not very good and will not have the rail weighting or connectors for a modern system. Using it is only going to cause trouble.
You would be much better off selling the full machine as it is for whatever you can get, then put this money towards the new parts. There is nothing in that system that could be reused unfortunately.