Hi, I have a PC with 2 nics installed.
NIC 1 is connecter to a gbit network with static ip 10.0.0.x and connects to the internet through a server 10.0.0.1. This server is connecter to the internet router and I can access the internet through it.
NIC 2 is connecter to the internet router running DHCP so NIC 2 has ip 192.168.1.y.
Can I use both internet connections? NIC 1 through the server with spam filtering and NIC 2 through the router without filtering? Is it possible to use Internet Explorer on one connection and Firefox on the second connection?

Not in the way that you have described your current situation but it is possible to some degree - if you create a Virtual Machine on your computer using something like VMWare or Microsoft Virtual Machine. This would be like running two different computers on the same hardware. You can assign one virtual machine to one network and the other virtual machine to the other network.

The problem with what you are trying to do is that your Network Adapters advanced settings include a priority level. One of the network connections has priority over the others (in Win XP, go to Network Connections, Advanced, Advanced Settings). Only one of those connections can answer requests for Name Resolution. So each time you go to a web site, the NIC with the highest priority will answer first. And if you have multiple resource types for name resolution, they will be answered in the following order: Local HOSTS file, local DNS cache, DNS server, then WINS server.

To get around the limits of a single Gateway Address, static routes must be used. And this is limited to the addresses or network ID's that they are configured for. This would not help you with the requirement of running two browsers. Both are making their web requests using the same ports. HTTP uses port 80 by default.

Note: Some people make use of the local hosts file as a basic filtering system for their children. The web sites that you do not want them to have access to can be added to the local hosts file to resolve to 127.0.0.1. Your web requests for the domain names in your host file will resolve to the local loopback address instead of getting the name from your DNS server, etc.