arcgis desktop - How to combine data from overlapping polygons?

Here's what I'm working with:

• Shapefile of the current 32 Congressional districts for all states


• Shapefile of the tract boundaries for Texas


• A DBF format table of Hispanic counts and proportions for Texas census tracts (joined to the tract boundaries)

Using this data set, I'm trying to determine the following based upon the centers of the census tracts:

1. Total Hispanic population for each Texas Congressional district


2. Hispanic proportion of total population for each Texas Congressional district


3. Count of majority Hispanic census tracts for each Texas Congressional district


4. The shape index value for Texas Congressional district

I'm also trying to create a map applying shading symbology to display the number of majority Hispanic census tracts for each Texas Congressional district.

My problem arises when I try to combine the attribute data from the census tracts with the congressional districts. I need to combine all of the tracts within individual congressional districts and sum up their Hispanic populations. Dissolve isn't working, because the congressional districts and census tracts don’t share any common attributes. When I join the shape files spatially, most of the attribute data gets lost.