DC has written
The folders @user Pro1 is talking about are in your CS2D install folder in
sys/cache/avatars
(I guess you can actually delete that entire folder with all its content)
Also make sure that CS2D isn't blocked by any firewall. Avatar download requires a HTTP (TCP) connection so it's possible that gameplay (UDP) works while HTTP is blocked.
On Windows add a program exception for CS2D.exe to Windows firewall
(link)
If you have additional firewalls (software or hardware/router) you might have to add exceptions there as well.