Unfortunately, I see no mentions of similar issues online. Try disabling your VPN or Proxy, in case you're using one. Another possibility is that you're trying to use the app from a location such as your workplace where the ICQ servers may be blocked.
Lastly, if you're using a very old device or an old Android version, the ICQ app may not support it. According to its Google Play page, the app requires Android 4.0.3 or a newer version of the OS to run.
