What do you mean by "proceed with the next one"?
You are doing the <cfif> somewhat correctly (you don't need the # signs in a <cfif>, and you have too many "or"s). Do you have this code in a loop or something, and want to check all fields dynamically?
You could do something like this:
<cfloop from="1" to="50" index="i">
<cfif NOT structKeyExists( form, 'startDateName' + i ) OR form[ 'startDateName' + i ] EQ "">
<cfoutput>Form element #i# is not defined or empty</cfoutput>
<cfoutput>Form element #i# is defined as: #form[ 'startDateName' + i ]#</cfoutput>
Or if this code is supposed to handle a grid of form fields, you could have a nested loop inside. The outer loop does rows, the inner one does columns (or however you want to do it).