I had this error message with Corp version 1.1.1 and 1.1.2
I did not have this issue with 1.0.6.

To replicate:
go to http://<domain>.com/ (this is never an issue if you are logged out of the system)
Log into the collab system.
While still logged in, go back to http://<domain>.com/ and it will come up with the below error message.
I can go to http://<domain>.com/public after being logged in to bypass this error message.

the $compile_dir 'ENVIRONMENT_PATH/compile/' does not exist, or is not a directory. 
Error params: 
File: NULL  
Line: NULL  
Backtrace: 
#0  Error->__construct(the $compile_dir 'ENVIRONMENT_PATH/compile/' does not exist, or is not a directory., 1) called at [C:\server\www\collab\angie\classes\errors\SmartyError.class.php:26]
#1  SmartyError->__construct(the $compile_dir 'ENVIRONMENT_PATH/compile/' does not exist, or is not a directory., 256) called at [C:\server\www\collab\angie\classes\smarty\Smarty.class.php:1096]
#2  Smarty->trigger_error(the $compile_dir 'ENVIRONMENT_PATH/compile/' does not exist, or is not a directory., 256) called at [C:\server\www\collab\angie\classes\smarty\internals\core.write_compiled_resource.php:20]
#3  smarty_core_write_compiled_resource(Array ([compile_path] => ENVIRONMENT_PATH/compile/\%%6F^6F8^6F82F08D%%index.tpl.php,[compiled_content] => <?php /* Smarty version 2.6.16, created on 2008-06-19 20:16:54
         compiled from C:%5Cserver%5Cwww%5Ccollab/application/modules/system/views/dashboard/index.tpl */ ?>

 
Autoglobal varibles: 
$_GET: empty  
$_POST: empty  
$_COOKIE: array(4) {
  ["__utma"]=>
  string(64) "265406158.1014781309204401000.1211478524.1213722627.1213725649.3"
  ["__utmz"]=>
  string(70) "265406158.1211478524.1.1.utmcsr=(direct)|utmccn=(direct)|utmcmd=(none)"
  ["PHPSESSID"]=>
  string(26) "ttm5imi16sig80c4hs3hs9fr96"
  ["ac_ActiveCollab_sid"]=>
  string(40) "8q9ECl9BHdOrXKvCra57NcQm66FmUtTBmEm24ip6"
}

 
$_SESSION: 

Verified the defaults.php and config/defaults.php

I do not use FTP to upload the files. I remote desktop to the Windows server, and then extract the Zip file localy and transfer the files that way.

I double checked the contents of the config/defaults.php and that is the exact contents.

I have a vague idea of whats going on here, but nothing specific.

I have the following lines at the end of my config.php

- require_once 'defaults.php';
- require_once 'license.php';

I re-downloaded the latest collab version, and followed your above instructions. I also cleared the cache folder of all cch_acx_* files and I emptied the compile folder.
Same results as before.

Would it possible to send you my files somehow? Or I can provide you with limited access to my system if needed.
Let me know what you need, and I will provide you with it.

Thank you