diagnosing the motors shouldn't be too difficult as long as you can get access to them. Power steering is usually easy to access, the hydraulic and drive motors may be the challenge as you generally have to pull the battery out and remove a panel/plate the battery sits on.

Sorry I have taken so long to acknowledge you're kindness and input. I don't believe it's the battery itself. From this input I've received from you I believe it may be a motor. It cuts out and it won't run until I turn the steering wheel then the motor will start up. Now when I accelerate I can hear and feel a drop in the power. I have a truck to load Tuesday and I haven't used the lift in a couple days and I'm skeptical about trying to load a truck with it. Would the motor be hard to diagnose and replace?

yes, with electric lifts when theres smoke its usually a bad thing :o)
look for burned contactor tips, wires, melted connections on the control unit. If the smoke was coming from the rear panel as you said you should see something burned right away. With the contactor tips the directional ones can sometimes be a little tricky to look inside, but if you see melted metal or a lot of black suit around them or any other ones that's a sign they have been hot and arcing, melted ones are pretty obvious. In some cases the power steering contactor is hidden behind a component like a fuse panel (GE 100 panels are built this way) and you'll have to pull some things out of the way to see it unless you have a very bright flashlight and a mirror that can get you a good angle view on it. Some of these units were built with a sevcon control system so the component layout is different than a GE100. Both are similar but the GE panel has a couple of extra components according to the panel contactor schematic.

Now burnt wiring can be pretty obvious if the plastic covering is burned off but sometimes it can be just slightly melted and not quite as noticeable if you turned it off before it got destroyed.

Just take your time and look at everything.

Now if you do not find anything burned in the panel area since the smoke was coming from the back panel it could be something underteath the battery like a motor or some wiring under there because the main power cables run in a harness galley underneath that area, also some motors are mounted underneath either on side compartments or directly underneath the battery. Sometimes hydraulic motors are also mounted underneath there as well.

Any time there is smoke there is a problem. Have you opened up the back to inspect? Check all the cable connections an look for any signs of heat. Problem could be as simple as a poor cable end crimp or it could be a short inside the controller or a bad set of line contactor tips. A bad battery can cause all kinds of problems. If your voltage drops very quickly this can cause a fast rise in current which will generate heat.