I have two different gateways can i use two nic cards for one desktop

Assuming the gateways are on different subnets, just assign an IP address from each subnet to each card. If each subnet has it's own DHCP server, you shouldn't even need to assign addresses to the cards as they will pick them up themselves.

It will work, but you won't get a speed increase unless you use a load balancing server like Server 2003 or newer. Or a load balancing Router.

I guess, the separate networks for applications and internet are designed like that by a system / network administrator? In this case it's not a good idea to connect to both networks with one machine. At least you should switch of the 'internet connection sharing' in windows. Otherwise the internal network is reachable from the internet trough your machine.