Is there any way to capture Javascript events (e.g. button click) with Chartbeat?
Unfortunately, no...Chartbeat doesn't track JavaScript (or Flash) events. Assuming you require "realtime" analytics, check out Woopra (free) and Clicky (not free).
(If you don't care about "realtime", any of the major web analytics platforms are able to track just about anything you can pass to the tag. Webtrends (not free) is extremely powerful for custom reporting, and can handle very complex tagging needs. Google Analytics is fairly weak in those respects, but it's free.)