Hi Foo Bar
GFCI receptacle installed on an ungrounded circuit provides safety protection but it does not ground the equipment plugged into it. So, any sensitive equipment (for example your PC) with a three prong plug requires the receptacle it is plugged into to be grounded.
Another issue is the wiring between the circuit breaker and the receptacle. If it is a single circuit with a single neutral and hot wire between the breaker and your GFCI outlet used for PC, the outlet should properly trip in case of a surge (again, no ground protection).
However, if it has been installed on a shared neutral circuit (one neutral wire and two hot wires), for the GFCI to respond properly in case of a surge, those two hot wires must be installed on a two-pole circuit breaker, or all of the outlets at the end of the other circuit must be GFCI type. Still, there’s no equipment ground protection.
Therefore, it would be safer for your equipment to use some other outlet receptacle that is grounded, or try to ground the existing one.
Check GFCI without ground post