cdaddy,
If you have time, you can certainly try and get a new certificate.
Otherwise, I think this would not be a show stopper, as long as
you have your parents' names IN EXPANDED FORMAT either on the last page of your passport, or your school leaving certificate
( normally the father's name would be mentioned ).
These you can show as secondary evidence.
Apart from this taking an affidavit from your parents, showing their full names, should also be OK . ( by the way, if you take an affidavit, ask them to get it notorized ).
Raju