Make sure that the “Keyjazz” icon is ticked. “Keyjazz” lets Renoise register more than one note being played at once, so you can do chords. (If you want to record a chord, make sure you’re in record mode and then hold down left shift whilst playing the chord.)
When playing your keyboard, make sure that the record button (the transport button with the red circle) isn’t depressed, otherwise Renoise will stagger your notes into the slots when recording but not playing, like a step sequencer (as opposed to recording notes in real time, when it’s playing whilst in record mode). You can also tell you’re in record mode by a red border around the pattern editor. If either of these things are present, press the escape key to turn record mode off.
If both of these things are done, you should be able to stroke the keys and get a sound being played back without seemingly odd surprises.