Still not quite right... which kind of tells me what I need to know...
Go to View -> Organize Tests.
Those are your test items. when you run a project, this is what TestComplete (and TestExecute) use to determine what to run in what order. It can be very simplistic (as it is in my case) where you have one TestItem that launches a framework structure to execute a seriest of tests... or it can be complex with nested groupings and dependencies and such to structure the flow of your project.
No matter what... this is where the Test Items live... and if a test item (in your case ProjectTestItem1) is mis configured, you'll get the error your reported in TestExecute indicating that the element cannot be found.