Check box formula and summary

My spread sheet has 10 columns, and each text heading has a numeric value as well. There are 12 rows listed, each being a hospital. I have a check box in each row/column and what I would like to do is the following:

1. When the box is checked for a hospital, it means they offer the service represented by the title of the column. Lets say the value attached to that title is 5I want the check box to remain and remember the value.
2. I would like to sum the hidden values both vertically (row 13) and horizonally (row 11) after all boxes have been checked (or not).

Is this possible?? I have attached an abbreviated sample. Thanks for yoiur help.