Vim - how to join lines using matching pattern

I have a txt file that contains contact info for businesses. Currently, each line contains a different piece of data for the business. I'm attempting to construct a pipe-delimited file with all the info for each business on a single line. The catch is that there are a different number of lines for each business. So the file looks like this:

Awesome Company Inc|
Joe Smith, Owner|
Jack Smith, Manager|
Phone: (555)456-2349|
Fax: (555)456-9304|
Website: http://ift.tt/1Ugz4Xg [HYPERLINK: http://ift.tt/1RZaQTZ
* Really Cool Company|
* Line of business: Awesomesauce|
Killer Products LLC|
Jack Black, Prop|
Phone: (555)234-4321|
Fax: (555)912-1234|
1234 Killer Street, 1st Floor|
Houston, TX 77081|
* Apparel for the classy assassin|
* Fearful Sunglasses|
* Member of the National Guild of Killers since 2001|
* Line of business: Fuhgettaboutit|

etc.

So I can use :g//j to join lines within a pattern but I'm having trouble working out what the pattern should be. In the example above, lines 1-9 need to joined, and then lines 10-19.

The key is the lines that begin with 2 spaces and an asterisk: " * Line of business"

The pattern should basically say: "Starting with the first line beginning with a letter, join all lines until the first line after the last line beginning with '\ \ *\ ', then repeat until the end of the file."

How would I write this? Should I maybe do it in two steps - i.e., is there a way to first join all the lines starting with letters, then all the lines starting with "\ \ *\ ", then join each resulting pair?