TestComplete cannot find process

This is, most likely, a timing issue in that the process is not present when the "Exists" property is checked.  If you think about it, you can't call the "Exists" property of an object if there is no object.  You can't check ANY property of an object that does not exist.

If you're looking at testing the process existance, this is the better code to use (JavaScript):

var processExists;
var webServiceProcess;

processExists = Sys.WaitProcess('WebService.Service', 20000).Exists
if (processExists){
    webServiceProcess = Sys.Process('WebService.Service');
}
else{
    Log.Error('The WebService.Service process did not resolve within 20 seconds');
}

See https://support.smartbear.com/testcomplete/docs/reference/test-objects/members/sys/waitprocess-method-sys-object.html