As has been mentioned, what Moodle does is deliver e-learning, which is not what your client is looking for. In terms of other open source options, you could look at Drupal or Joomla as a CMS. I've only used Joomla - it is powerful but there's something of a learning curve, and I didn't warm to it at all. From what I've read Drupal has an even stiffer learning curve (though it is more stable for larger sites).
Magento is an open source shopping cart - though you may need the Enterprise edition, which costs, if your client wants to be able to export to their existing accounts package.
You can join Joomla with Magento to provide a "single log on" - I haven't done this, but I have joined Joomla with Moodle on a non-production site. This might be useful if your client wishes to offer elearning in future. It works reliably enough, but I know there have been some security concerns about Joomla's "Jfusion" bridge recently. You may be better off exploring Moodle 2 if you want to join Moodle with other products. (You can also join Drupal to Magento, but I haven't tried Drupal's Magento plugin).
Magento also joins with Wordpress, and there are several very good calendars for Wordpress (many people use Wordpress as a CMS rather than a blog these days). If your programmers can handle the accounts side that might be an option as Wordpress is very user friendly.
Non-open source : look at Trumba. It's not free but not 10k either, and will handle pretty much all of the calendar side. It can run on more or less any site, so you could combine it with any of the above open source options.
In short, keep Moodle in mind if your client later needs an elearning package - at the moment they don't, so it isn't at all suitable for this particular gig.