I solved this by creating the following rule. Hopefully it will help someone else who is a newbie.
Note that although I have 11 required fields I chose to set rules on only the 4 fields that are likely to be the culprits.
Set Condition:
txtField1 is blank or
txtField2 is blank or
txtField3 is blank or
txtField4 is blank or
Action:
Set a field's value: Status = "Request"
Show dialog box message:
"Actual travel dates or Event dates are blank.
Please revisit section A1 and B1 to ensure START and END dates are entered and click Submit button again.
(A message box will follow this message: "Some Rules were not applied" . Click OK to close it and continue.)"
The problem with this will be if any of the other 7 required fields are blank, the submit button resorts to its old behavior so I may have to go back and add all fields to the rule. There is a limit of 5 conditions on a rule so I suppose I would have to create 3 sets of rules to accomodate all 11 text fields being blank.
Also it might be better to remove the "Cannot be blank" check mark in a fields properties to avoid the 2nd message popping up (if a rule/condition catches it that is).