I used to have blackice defender as a firewall, but since I installed a router I see that I get no more attacks on my blackice defender. Does the router act as a firewall now?
The quick response is 'yes,' but you need more than a router acting as a firewall for security.
A border or perimeter router, when configured properly with an Access Control List (ACL) can filter inbound and outbound traffic and therefore "act as a firewall." However, a router's primary role is to forward packets across networks and not to replace a firewall, and vice versa. With that said, a border router can block unused services and ports that further protect your personal firewall.
Hopefully you are still using a PC firewall, at a minimum. Consider closely inspecting logs for firewall attacks and address these attacks with Black Ice Software to see if they offer a security hotfix.