OK, in the order....
1/ Theoretically, you should have no problem to run my test project (it's really a very, very, very basic project).
Have you :
- unzip all the files (7 files),
- start the project (double click on YourTest.lpr or on YourTest.lpi to start Lazarus with it),
- Run -> Build menu in the Lazarus IDE to compile it,
- and finally Run -> Run (or F9).
2/ I've downloaded and tested your own project (MainUnit.zip). Everything is working correctly here (see capture).
3/ As you've deleted the executable file, you must re-recreate it in order to be able to run it. So, in the Lazarus IDE, menu : Run -> Build.
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Are you using an old version of Lazarus/FPC (current release version is 1.2.6/2.6.4) ? Did you get any trouble when installing it ?
Because you should now be able to compile and run your own test project without any problem. I can't see any reason to get an error.