You probably are having DNS conflicts with the router, since a router acts as a DHCP/DNS server. You need to either let your router control the DHCP/DNS and plug it into your client and then bind the client to the AD machine, or turn it off in your router and let the server handle it.
The problem most likely is (and this is a guess by the way) that your client has to perform a DNS look up on your network to find all available servers to log into, and since the router is not an AD server, it goes on to the next server. Which is why it takes so long. You remove the router and you take out any DHCP/DNS conflicts, and thus it works very fast.
You should pick up a book on basic domain level networking, it explains all of this, and while it is possible to have more than one DHCP server on your subnet, it does take some special configuration to do so.
