Disable the auto-updater in the settings of the launcher and try again.
If that doesn't work, try to create a shorcut of RelicCoH.exe and add some parameters:
-dev means mode to run mods.
-nomovies means skip the movies played when starting the application.
-mod which mod are you playing.
-novsync vertical sync disabled.
-notriplebuffer Triple buffer disabled.
You need at least the first three. And the shorcut should be something like:
"C:\Program Files\THQ\Company of Heroes\RelicCOH.exe" -dev -mod Eastern_Front -nomovies
If you want to add some other parameter besides these three feel free to do it.