First of all, have you contacted Trados Support? Given that the vast majority of soft license users doesn't have a problem, the problem might, in fact, be related to your system.
It seems like being connected to Wireless in a public library changes the registration parameters and make my licence invalid.
Does the problem persist when you disconnect from the WLAN?
Note the restriction applicable to Freelance versions (as outlined on TranslationZone):
SDL Trados 2006 Freelance is designed to work in a single user environment and thus only one instance can run on a network at any one time. SDL Trados 2006 Professional is required in order to share translation memories on internal networks (LAN) and provide multiple users the ability to simultaneously work on a network and have access to the same translation memories.
When Trados Freelance detects more than one Freelance instance in the same network, it will switch to demo. Could it be that someone else is using Trados on the same network?
On a personal note, as much as I can understand your frustration about software problems (having been there myself), this doesn't exactly get your problem solved.