First of all, if you have auto climate control (ACC) you have a blower control module and do not have relays for the blower. The module will fail sometimes due to high amperage draw from the fan, but not always. I have seen them fail even with a new fan motor. It does not hurt to test the amp draw on the fan motor before you replace the module. It should be around 17-18 amps on high speed and not more than 22. If it is pulling more than 22 amps, replace the motor.
The "blower control module", is located on top of the fan box under the fuse and relay section on the firewall. It has two wiring connectors connected to it and usually three screws holding it in the box. You can get a new one from any dealer for around $150.00. It is such a common problem on Buicks and other GM cars with auto climate control & fan control, that the dealers usually keep a good supply on hand. You can also check your local salvage yard, (about $50.00) they usually have some at the front counter. Be careful to insist on the same part number as the one you have removed if buying from a salvage yard. (The part number will be on the module). GM made four or five different controllers that look the same, however do not have the same number of wires or the same functions.
You do not have a relay for the blower fan because the controller module sends variable voltage to the fan motor to control the speed. Usually the resistors fail in the module and the default voltage is 12V direct to the blower, unswitched, therefore, your blower runs all the time unless you pull the fuse, disconnect the battery, or pull the plug on the fan itself. They also fail in the no run mode, or intermittent mode. The fuse is also located on the firewall with the relays. Pull the cover off and look inside the cover to locate the correct one. It is a 25 or 30 amp fuse.
I have also found that Advanced Auto parts (part# RU304) and others are now selling a new module for around $100.00.
Shown below is a pic of the module;
