A couple of thousand check boxes !!!
So whats generating these check boxes and what is the data and how is the data field set up? Are you sending a very long stream to one variable?
Production is not the same as deployment server and whilst you may have something running fine on a 5.2 branch, 5.3 has changes to it and this may be whats causing the problem. I was annoyed that they dropped SQLite2 from PHP and offered no legacy option in SQLite3 which has likely left millions of users whose sites use SQLite2 and with the host upgrading to 5.3, many a site is now stuffed...
Anyway, in my opinion your issue is because of 5.3, do you have the option to roll back to a previous version on the deployment server? Rule out that its a PHP issue or not.
The option you have is to install a webserver, PHP5.3 and try it locally with 5.3.