I wouldn't worry about the 1 month limit, the trial license can be extended. However, be advised that you may not publish or use any results obtained with a demo version of ATK for real work, like a PhD thesis etc.
Your problem is unusual, and I don't have a clear idea what might be the problem. I would make sure to place the VNL-related parts of the PATH up front, as the first entry of the PATH. Also, try (just to make sure) to reboot so that the PATH takes effect. Sometimes the location of DLLs is cached.
Also, you can try to use the vnl/bin directory as the startup directory for the shortcut.
Have you made sure the license is installed properly? On the same command line as you used for running the DLL, write
echo %LSHOST%
echo %LSERVRC%
dir %LSERVRC%
and verify that the license file (for 2010.02) is correctly identified. Another way to test this, is if you can run ATK (the command line version), by executing "nlpython" on the command line (or use the corresponding entry in the Start menu).
It's not the path which is important but the file. So run
chcon -t texrel_shlib_t FILE.so
for each FILE.so which generates an error message (in your case it's /opt/QuantumWise/atk-2010.02/vnl/lib/python2.6/_NLLicense.so as you can see from the error message you posted). You may need to do this for several files, but the error messages will tell you which ones.