program rsem cannot find the trans.fa that I'm using as input (even though it's there). Oddly enough, when I run the code again using the konsole and not via Galaxy, it works fine.

That sounds like a classic "permissions issue".

One way to track such issues is to add a couple of lines to the top of the script (rsem.pl in this case), that display the permissions available for each component of the path(s). Eg.

sub checkPathPermissions {
    my( $path, @bits ) = split '[/\\]', shift;
    $path = '/' . $path;
    while( @bits ) {
        print STDERR "$path: ", join ' : ', stat( $path );
        $path .= '/' . shift @bits;
    }
}
[download]

Note: That untested code; to illustrate the suggestion only.

If you add that to the top of rsem and call it on each of the input paths; then run it from your console and via galaxy, the difference between the two runs will probably go a long way to diagnosing the issue.