At the front of the machine beneath the sewing platform you'll find the complete number of your machine.
To get the top off, cover a screwdriver with a piece of fabric, slip it under the edge of the top, and gently pry it upwards. I work from the back of the machine "just in case".
I wouldn't get rid of the Kenmore until you're positive you don't want it. 12 stitches to the inch is the max on mine, but I'm fine with that.