Well, the validation rule does not allow an opportunity to save if it meets the criteria below.  I am totally at a loss as to how to work around this.  The field that I update on the opportunity via the trigger has nothing to do with these validation rules.  I have been messing around trying to see if I could write something in the validation rule that will allow everything to run and update the Cost field, even if the rule evaluates to True, but I don't think I have enough experience to figure this one out.  Whatever the solution, it needs to work both from data loader and the user interface.

I really, really appreciate your help on this!!!

Error Message:  Close Date must be in the FUTURE - Please change Close Date

AND(
OR (
ISPICKVAL(StageName ,"Job Dispatched"),
ISPICKVAL(StageName ,"Waiting for Approval"),
ISPICKVAL(StageName ,"Searching for sub"),
ISPICKVAL(StageName ,"Waiting for Approval"),
ISPICKVAL(StageName ,"Approval Received - Need Contractor"),
ISPICKVAL(StageName ,"Priority - Searching for Sub"),
ISPICKVAL(StageName ,"Proposal/Price Quote")),
CloseDate < TODAY(),
IF(OR(ISNEW(), ISNULL(Id)), if(ConnectionReceivedId =null, TRUE, FALSE),NOT(AND(ISCHANGED(ConnectionReceivedId), NOT(ConnectionReceivedId = null)))),



NOT(Contains($User.Alias, "pnet"))
)

Additionally, this validation rule is also causing the trigger to fail:

AND(
ISPICKVAL(PRIORVALUE(StageName),"Closed Won"),
NOT($Profile.Id = "00e30000000c8cX")
)

Error Message
You cannot edit this opportunity as all opportunities marked "CLOSED WON" are locked from editing. If a change must be made to this record please discuss with Operations Manager or Supervisor.

The trigger updates a Cost field on the opportunity, everytime a custom object Work Order is modified:

trigger triggerWorkorderOppUpdate on Work_Order__c (after insert, after update, after delete) {

    //************************************************
    // Build a LIST of Opportunity ID's that will
    // need recalculating
    //************************************************
    set <id> oppIDs = new set <id>();
    list <Opportunity> opportunity = [SELECT ID FROM Opportunity WHERE ID in:oppIDs];


    
    if(Trigger.isInsert || Trigger.isUpdate){
        for(Work_Order__c w : trigger.new){
            if(w.Opportunity__c != null) 
                oppIDs.add(w.Opportunity__c);
            }

            }

      // INSERT/UPDATE Trigger

    if(Trigger.isDelete || Trigger.isUpdate){
        for(Work_Order__c w : trigger.old){
            if(w.Opportunity__c != null){
 //              if(!oppIDs.contains(w.Opportunity__c)) 
                oppIDs.add(w.Opportunity__c);
            }
            //           w = [select ID, Opportunity__c from Work_Order__c where Opportunity__c in :oppIds];
        }
    }  // DELETE/UPDATE Trigger

    if(oppIDs .size() > 0) {

        Map<ID, Opportunity> opps = new Map<ID, Opportunity>([Select id, Estimated_Cost__c from Opportunity Where Id in :oppIds]);  
     
        Opportunity d = null;

        for (AggregateResult dr : [SELECT Opportunity__c, SUM(Cost_WO__c) SubPO FROM Work_Order__c WHERE Opportunity__c in :oppIds GROUP BY Opportunity__c]) {
                
            String dID = (String)dr.get('Opportunity__c');
            //get record or create one
            
            if(opps.get(dID) == null)
            d = new Opportunity (ID=dID,
                Estimated_Cost__c = 0);
                
            else
            if(opps.containskey(dID))
                d = opps.get(dID);
                
                    
            // update the summary total fields on the opportunity
            Decimal po = (Decimal)dr.Get('SubPO');
                    
            d.Estimated_Cost__c = po;
                        
            opps.put(dID, d);
        }
        //commit the changes to Salesforce
        
        update opps.values();

    }

}