Simple PHP & Ajax debugging

I have just moved my website to a new web host, and a number of pages are no longer working correctly. Some of this is due to MySQL credentials being hard coded to the old IP which need updating. I also have some Ajax scripts which are no longer working. I am sure it is a very simple fix, but I need someone to look at the pages and tell me why the scripts are failing.

If you do a good job, there will be many additional jobs in the future to help build new functions, pages, etc. on my website.