Thanks for the input Dan. The SSIS package consists of 4 Transfer SQL Server Objects Tasks. These tasks are not joined by any success/failure/completion constraint. They all run simultaneously. Two of the task objects connect to seperate databases on one source server while the other two task objects connect to seperate databases on a second source server. The source servers are both running SQL Server 2000. What I'm trying to do is copy a select few tables from each of the 4 databases (on 2 servers) into one destination server and 4 different databases. This really should be something very simple, and indeed our old DTS 2000 package that runs this on our live server has no problems at all. But for some reason no matter what I try, I keep getting errors when doing this under SSIS.
To answer your other questions, yes the tasks do run fine when I test them individually in Visual Studio. The problem only seems to come in when I import my package into SQL 2005 and setup a scheduled job for that package to run. I import the package into SQL 2005 IS using the security level of letting SQL Server roles / users manage security. I then configure the job to run it and set a test schedule a couple minutes ahead of current time. The job kicks off and within 3 seconds usually it fails and dumps out with the message in the original post.
I tried searching my IS package from Visual Stuido using the method you suggested and it did not find any reference at all to "LocalApplicationData". I searched the entire solution. I know I've never specified anything like that either as I built it. It seems to be some weird generic system generated error than anything specific.