OT: vpn questions (stops using my internet connection and starts using the gateways?)

[Christopher J. Bottaro]

i installed cisco's vpn client for linux and i successfully connected to my
work's vpn gateway.  the problem is once i'm connected, my ip address is
changed to vpn gateway's ip address and my internet connection becomes very
slow.  i'm assuming this is because when i connect to sites on the
internet, its actually the vpn gateway thats making the connection, then
forwarding the data to my computer.

i always thought vpn was like that i could be locally connected to an
external lan, while still being connected to my lan at the same time.  am i
wrong in thinking this?

i want to use vpn to connect to a few machines on my work's lan, not use my
work's internet connection.  can i achieve this somehow?

thanks for the help and sorry i didn't know where else to ask this...this
list seems to answers for anything/everything regardling computers...=)