When installing W3TC after BPS is installed you need to do the steps in the link below.
http://forum.ait-pro.com/forums/topic/w3tc-activation/#post-5673
BPS Pro is a very advanced plugin that has built-in troubleshooting capability and turn off / turn off settings for all BPS Pro security options and features. You do not need to uninstall the BPS Pro plugin to turn everything off in BPS Pro. When you uninstall BPS Pro all of your BPS Pro database options and settings are deleted. See the general troubleshooting link below.
http://forum.ait-pro.com/forums/topic/read-me-first-pro/#bps-pro-general-troubleshooting
I received another email from you stating that things were working briefly and stopped working again.
At this point do these steps:
Deactivate the W3TC plugin if it is activated.
Reinstall BPS Pro if it is not installed. Use the Setup Wizard to setup BPS Pro again.
Do the W3TC steps in the link below. Note: I do not recommend that you use Minify in W3TC – it is very problematic.
http://forum.ait-pro.com/forums/topic/w3tc-activation/#post-5673