How to connect to two LANs?

Hello How to connect one RJ-45 cable from a LAN to my Windows 2000 computer and one outlet from another LAN to my computer and to another computer for my compuer to use resources of both LAN's and the other computer use only the second LAN? I have one installed Network Card and a Network Switch - 3Com OfficeConnect Switch 8. I can get access to both networks interchangeably now by inserting the RJ-45 cables to my installed NIC. IP address and address of DNS-server are got automatically in TCP/IP properties. How to get access to both networks at the same time? What is a cheaper way to get resources of the both networks for my computer?

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