TheStud,
Your problem is pretty direct. On your local machine your text file is probably located in the same location as you applet (or has default policy file set to AllPermissions) so you won't have any problem.
When you try it from another machine its another case altogether. We all know how Java prides itself on being a secure platform such that malicious code cannot take advantage of the system running the Java app. As such the applet is not given the permissions to run amok and go thru the files on your machine or your network.
To resolve this you have to explicitly set permissions giving permission to the VM under which the applet is running OR alternatively you can sign the applet, in which case the browser should allow the applet to access the file.
But I think the best solution would be to use ONLY the file name ('mydata.txt') without the extension when trying to open/access the file. That way if the file is in the same directory as the applet the applet will be able to open/access the file without any need for the above security details. I think this would preferred.
Let me know it this helps.
Akanimo.
P.S. - Better change your username to your own name (or alias) before the bartenders/sheriff get on your case