Bottleneck encountered returning records for my grid
Obvious slowdowns  


for each property of NameValueCollection which is set, the condition can ommit the ==0 check.  
you are sorting the results 2 times  
using .Count(), but this seems to be needed.  
calling unneccessary .ToList() on parents  
posibly unneccessary call of .ToList() on result. Here you should check if CustomerPaged.aaData can take an IEnumerable&lt;MODIFIED_DATA&gt;


Naming  


result is an IEnumerable&lt;MODIFIED_DATA&gt; so the plural should be used -> results  
the kind of hungarian notation you use is seen as bad practice  
local variables should be named using camelCase casing  


General  

Consider to extract the "index" strings, like "sSearch_0", into class const variables