SQL Syntax Error

Your From date check appears to have a random '20' on the front of it, which won't be helping. I also can't see the point of aliasing a table with its actual name. Try using:

.CommandText = "SELECT HPD_Help_Desk.Incident_Number, HPD_Help_Desk.Description, HPD_Help_Desk.First_Name, " & _
         "HPD_Help_Desk.Last_Name, HPD_Help_Desk.Priority, HPD_Help_Desk.Status, HPD_Help_Desk.SLM_Status, " & _
         "HPD_Help_Desk.Company, HPD_Help_Desk.Last_Resolved_Date FROM HPD_Help_Desk " & _
         "WHERE (HPD_Help_Desk.Company='DCWR') AND (HPD_Help_Desk.Status>='Resolved') " & _
         "AND (HPD_Help_Desk.Last_Resolved_Date>{ts '" & from & "'} " & _
         "And HPD_Help_Desk.Last_Resolved_Date<{ts '" & untill & "'})"

and see if that helps.