One problem is that in your button, the press attribute shouldn't be written as a merge field.
<ui:button label="Go" press="c.search" />
You also have a misspelling in your client-side controller. It should be:
search : function(component, event, helper){
You might be getting the message "component is not defined" because the variable was named "componet"
Also, you could also simplify you server-side controller if you wanted: (unrelated to the error)
public class CheckinCntrlr{
@AuraEnabled
public static String checkfoundevent(String ticketid1){
Ticket__c obj = [
SELECT Event_Product__r.Event__c.Name
FROM Ticket__c
WHERE Id = :ticketid1
];
return obj.Event_Product__r.Event__c.Name;
}
}