It turned out there were two issues here: first checkout stopped working, then the server ran out of space. I now have space on the server, but the checkout still isn't working.
It's a commerce site, and checkout worked fine until launch and now the process appears to be broken. I get this message in the Drupal error log.
Notice: Undefined index: field_extra_instructions in commerce_customer_profile_pane_checkout_form() (line 165 of /home/wholebox.org/www/profiles/commerce_kickstart/modules/contrib/commerce/modules/customer/includes/commerce_customer.checkout_pane.inc).
The site is wholebox.org and if anyone can help find out what's wrong, it would be very handy right now.
Could I have disabled an important module when trying to make it faster?