When I call for AC on the dash the clutch on the compressor doesn't engage. I disconnected the clip that connects the wire to the clutch and checked for voltage and there was none. People say that means I "need a new computer". But that seems drastic. And expensive. Is there some fuse that can be blown? Some broken relay?
There are several things that can keep the compressor from engaging
One of the most common problems is a low refrigerant charge, the low pressure switch prevents the AC clutch from engaging when the system is low on refrigerant.
Definitely check the fuses before replacing anything else. Your interior fuses should be on the drivers side as pictured below in a video from carcarekiosk.com.
The video shows a page in the owner's manual that indicates that a fuse connects to the "A/C Controller" titled "MIRR HTD". It is a 10 Amp fuse. Here is an image from the same video. (The panel is being held sideways).
Another fuse is under the hood on the drivers side titled "A/C Clutch". The picture below is from justanswer.com. Look at the lower left corner of the image. It's labeled "J".
Those are the only two fuses that I could find. You should check them both and any others that might be related, such as the blower fuse, just in case before you move on to more expensive repairs.