Running out of ideas here. If the network is OK in every other respect but you still cannot connect the browser to SlimServer on the same PC and there is no firewall geting in the way then SlimServer would appear to be at fault.
As for DHCP, I access my Belkin router through the web browser. LAN Settings is the first item on the menu at the left. DHCP on/off is in the LAN settings. Here you will also find the IP address of the router (inwards to your network), and the range of IP addresses from which to assign addresses to PCs, SBs, etc. as they connect.
The next menu option is DHCP client list and this will show you all the connected devices.
The only other thing you might conceivably have wrong is the channel number or SSID. There is also the possibility that you have interference from a neighbour on the chosen channel although if web surfing seems normally fast then probably not. That wouldn't stop SB altogether anyway but it might make it skip.
If you have an unsecured network (i.e. you are not using WEP, you should check the client list occasionally to make sure no one else is using your network.