3 Door locks not functioning with fob or key

Most actuators I have seen look the same. If it is them you could replace them with one of those cheap central locking conversions around. Here they sell for about $30. Worth a look. It may be wires or connections too.

 

Once the door inner linings are removed the actuators are not normally hard to change although I have no experience with the Prius.

Not even sure how hard the door trims are to remove but you do need to be careful not to break the trims.

Best way to get them off normally is remove any screws which are normally near the inner pull handle and opening handle (may be under plugs) then start at the bottom rear corner, pull out the trim and look for the clips, use a thin screwdriver to pry the clip away from the door. Wrap the shaft of the screw driver in electrical tape or use a plasic coated shaft screwdriver to reduce scratching of the door. If you have someone show you one door the others will be easier. Take your time, you should be able to do it without damage. Once all the clips are out front and back and along the bottom you can normally lift up on the trim to remove the top.

If you break one or 2 clips don't worry too much, make sure the corner clips are good, you can normally remove the clips from the trims, they are in keyhole shaped holes and slide out to arrange them so corner clips are good. You should be able to buy new clips from Toyota, just leave a back door trim off until you have all the clips or you can leave on or two clips off each door just not the corner ones.

To replace the trims, position the trim where it will go after putting the top hooks in place then put each clip into its hole then strike the trim in line with the clip with the ball of your hand. You don't have to hit it hard, about how hard you clap loudly. Start soft and work up. Make sure the clip is in the hole or it will break the clip or the trim. you know when they are in, they often click in. Put the clips in from the top of the trim at the rear of the door, work down then forward half way along the bottom then to the front top of the trim, down and back.

The lock actuators should be pretty obvious once the trims are off. Normally held to the door frame with 2 screws and there may be a clip or "S" shape rod, I don't know but normally pretty easy to remove, do one door before moving to the next. Start with the back door which isn't working then work toward the drivers door last.
Good luck with it.

A rider here, I repeat these instructions are pretty general and I have never had the door trims off a prius. I'm assuming the 2002 prius is similar to Corolla. There may be wires to unclip if there are courtesy lights or speakers in the doors.