Can't draw half cylinder with rounded ends

What Peter said. Or drag a right to left selection window around the outboard ends of the faces you want to get rid of and hit Delete.

AwW! I didn’t say that correctly-- You must hold down the shift key when you double-click to de-select. (I forget what my fingers are doing, it becomes second nature.)

I’m still trying to figure out how to create a cylinder with rounded ends. Is that possible in Sketchup Free on the web?

Yes. It’s possible. Draw a cross section of the cylinder and a circle for a path. Use Follow Me to extrude.
cylinder

Be sure to draw the round-ended cylinder object at a large enough scale (and with small enough counts of segments in the arc ends and the circle path) to avoid SketchUp’s limitations of very short edge lengths. Otherwise there will be mysterious holes at the “poles” of the hemispherical end caps.