I'm moving a site to a new host and keeping the same domain name. Seems the same unaltered htaccess file would work for me...

Here's what I've got:
------------------------------------------
DirectoryIndex index.php
Options +FollowSymlinks
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^/(.*)$ index.php?var1=$1 [L,QSA]
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The file is being recognized, as it properly going to index.php.

However, nothing else is working.

First, I'm having to use a temporary url to browse the site until we switch the domain pointers. Looks like:
http://myipaddress/~myusername/

This properly resolves to the index page.

These work on the old site:
http://www.mysite.com/index.php?var1=faq
http://www.mysite.com/index.php?var1=contact
http://www.mysite.com/index.php?var1=privacy-statement

Also on the old site, these redirect properly to the above:
http://www.mysite.com/faq
http://www.mysite.com/contact
http://www.mysite.com/privacy-statement

These work on the NEW site:
http://myipaddress/~myusername/index.php?var1=faq
http://myipaddress/~myusername/index.php?var1=contact
http://myipaddress/~myusername/index.php?var1=privacy-statement

These do NOT work on the new site...
http://myipaddress/~myusername/faq
http://myipaddress/~myusername/contact
http://myipaddress/~myusername/privacy-statement

Suggestions?