To look like your demo and show the upcoming events for the next 6 months:
http://demo.myeventon.com/event-lists/
SHORTCODE I USED:
[add_eventon title="Current & Upcoming Events" type="pe" number_of_months="6" event_count="5"]
Please give me the shortcode I need to make this work EXACTLY like the example (yes - I even used the example AS IS - and even without the cal_id)