Count Number Of Full Time Periods Within A Time Period

I have thousands of timestamps that have a start & end date and time in 2 separate columns. (one named start and one named end...)

I also have numerous set time periods that i'm interested in.. (about a dozen or so)

for example 01/01/2008 - 05/01/2008, 07:30:00 - 10:00:00

What i need is to be able to count the number of times the full time period i am interested (07:30:00 - 10:00:00) in falls in between the thousands of start and end timestamps i have. The time periods must also fall within the date range specifed.

So if my timestamps were
Start: 01/01/2008 06:30:00 & End: 02/01/2008 11:00:00, based on the set time period above, there would be a count of 2

and if my timestamps were
Start: 01/01/2008 07:05:00 & End: 02/01/2008 09:00:00 there would be a count of zero as there is not a full uninterupted timeperiod 07:00:00 - 10:00:00 between these timestamps.

and if my timestamps were:
Start 01/01/2007 07:00:00 & End 02/01/2007 10:00:00 the count would be zer as this is a year early!