SQL 2012 :: Generating Date Range Values (start / End Dates) From Month Columns With Boolean Values

I've got some records like this:

ID_________Jan Feb...........................Dec
0000030257 0 0 0 0 0 0 1 1 1 1 1 0

where each month field has a 0 or 1, depending on if the person was enrolled that month.

I'm being asked to generate a table like this:

ID_________ Start_Date End_Date
0000030257 July 1, 2014 Nov 30, 2014

Is there some slam dunk way to do this without a bunch of If/Then statements?

The editor compressed all my space fields, so the column headers are off in some places.