2004 Buick Rendezvous AC not working

Check the A/C CLU RELAY 51, located in the underhood fuse block (front of right wheelhouse above the battery)

Check the A/C CLU fuse (10A) located in the underhood fuse block (front of right wheelhouse above the battery)

Also check IGN 3 HVAC Fuse (10A), located in the Center Console fuse Box (in the floor console)

If all of those are OK, have a technician to check the pressures in the system, it may be low on refrigerant.

Yes. If those fuses are bad that would cause a "No Power" issue. However, remember that you bought this car used and sometimes people can "create" reasons for items not functioning, So keep in mind that this may be a problem which is more involved than simply a "disconnected" A/C system. Why would someone disconnect the a/c anyway? If it wasn't needed, it'd be easier to just not turn it on.

Did you check the fuses I mentioned to see if they have power to them? (If a fuse or relay is bad the A/C nor A/C controls will have power to them.)

Remember, the easiest way to check the A/C CLU RELAY 51 is to switch it with an identical one. (There likely is and identical one, in one of the underhood fuse boxes) If after the relay is switched the blower and A/C works them the relay is faulty and needs to be replaced.

If the fuses and relays check out OK, check for power at the RED wire of the blower motor with the ignition switch ON and the blower speed setting on HIGH.
If power is present, the blower motor is likely bad or the connection at the blower motor is bad. (Wiggle the connector to check for a bad connection).

Let me know how these checks go, then if needed I'll tell you what to check on the HVAC control unit.