I had a power outage (15hrs) in my town - The ac unit did not kick on after power was restored - I replaced fuses to the unit - checked the breaker - put fresh batteries in the thermostat (White-Rogers 1F80-51) The fan will operate but the compressor will not -

Were the fuses blown? Or did you just replace them?

Fan operates? Is this the fan on the outside unit OR the inside blower motor?

Have you checked to see if the wires that go to the compressor are burnt OR the clips on the ends that go on the compressor terminals are still there and intact. Also look at the capacitor and the associated wiring.

Many times a outage can also contain a surge and that can cause major problems with wiring let alone motors and compressors that contain a motor also.

Check the above and report back