Suitable ticket system / help desk software

I am looking for a database-driven ticket-system / help-desk platform (PHP?) that meets the following requirements:
-new ticket system requirements
-assign tickets to support personnel
-categorize tickets
-user database (support personnel)
-equipment/parts database
-customer database
-customer equipment?
-calendar where tickets are displayed (Microsoft office outlook calendar style)
-possibly tie in with QuickBooks?


I am currently using OS Ticket/Quickbooks/Office Outlook, but it would be awesome if there was something (preferably free) that integrates these all, or at least connects them, and can be hosted online.

thanks

FocalScope

You can have a look at www.focalscope.com, For quickbooks integration you can use their APIs to set up a pipeline no sweat.