I think the issue is from the windows 7 installation.
Could you try the VST version, using an other DAW (the free vsthost for instance : http://www.hermannseib.com/english/vsthost.htm
Once you have authorized it, it will be authorized for all the other formats/DAW
The code you received from us is the XILS 3 LE serial and isn't related to iLok (only the full version is protected by iLok)
About the windows 7 installation, you need to use an user accessible folder. The default folder displayed on the current XILS 3 LE doesn't work (c:/Program files/XILS-lab) and you must use an other one (for instance c:/Users/Public/Documents/XILS-lab)