Here's what to do:
1 - http://www.mfr.f2s.com/backup/
Save an uncompressed backup to your computer
2 - COPY that backup and put the copy somewhere safe on your machine.
3 - Download ALL your blog directories to your machine, including any images folders, plugins - the lot.
4 - Upload everything you got in (3) to the new domain.
5 - Open up the sql dump in a text editor. Using a 'find/replace' function, you need to change your OLD url to the NEW url.
For instance, if you were at http://divrom.com, then do a find of 'divrom.com' to be replaced with 'churchexperiment.com'
6 - Save the file - just SAVE, not 'Save as'.
7 - Import the file as detailed in (1)
8 - Be sure that the 'wp-config' has all the correct details
It *should* now work.
If when you try the import you get errors, it may well not be the export function that is wrong, but that there is something wrong inside the file itself. If that is the case, post back and I'll try to help from there - I have had that happen to me before, but it's been fixable in each case.