Perhaps this set up can be used:
A1:H1 contains these headings:
Question....Criteria_01....Criteria_02....Criteria_03....Score....Crit_01_Base....Crit_01_Base....Crit_01_Base
The Crit fields contain the base number for each criteria. Any Col_B through Col_D values will be added to the base.
Examples: 
Question....Criteria_01....Criteria_02....Criteria_03....Score....Crit_01_Base....Crit_01_Base....Crit_01_Base
Question1             1              1              1                         1             0                0
Question2             1              1              1                         9             9                0
The score is calculated using this formula, copied down:
E2: =SUMPRODUCT((B2:D2>0)*F2:H2)+SUM(B2:D2)
With that example, these are the results:
Question      Criteria_01     Criteria_02     Criteria_03     Score       Crit_1_Base     Crit_2_Base     Crit_3_Base
Question1               1               1               1         4                 1               0               0
Question2               2               1               0        21                 9               9               0
Is that something you can work with?