The launcher stops in the middle of downloading the mods.
If your AV is not on this list it could still potentially cause problems. Just like any software, we recommended you disable your AV while installing and running your launcher for the first time to avoid issues.
These Antivirus programs are known to cause issues when downloading the launcher.
AVG
Norton
McAfee
Avira Because of user input, Avira has apparently fixed the false positive. Update your AV.
If you are using one of these you will have to disable them or set the Technic Launcher as an exception in order to install it. They block it by default since they don't recognize it (of course). If that doesn't work, uninstall those terrible anti-virus programs and get one that doesn't get in your way constantly. We recommend if you're paying for any of the above AV's to stop immediately, uninstall them, and get a better AV. Microsoft Security Essentials, or Avast! are two completely free AV's that work far better then all of the above. MSE especially I can vouch for, having used it for years.
Did you try that?