I have VPN client (checkpoint) to connect to my company netwrok.  the
company has site-to-site VPN with other locations, and in order for me
to connect to these location, I need to get the site-to-site trusted
IP, and not my ISP IP [the real IP, should be the trusted IP].  How
can I configure my VPN client (or the VPN at my company) to ignore my
real IP from the ISP?

Please correct me if I am wrong but you seem to be asking
"I need my remote connection VPN to obtain a company (internal) IP
address in order to access the other sites connected through VPN"

If this is the case then you will probably need a router with NAT, it
will allocate an IP address to any VPN connections based on the DHCP
setup.

When connected to the network through the VPN can you ping the other
computers over the other VPN - by name and by IP address?

BB

When your VPN client connects, it will pull an IP address from
whatever pool your administrator has configured you to pull from, this
may be your companies DHCP pool, or a seperate pool reserved for VPN
connections.  Either way, if you are connected, you will be receiving
another IP besides the one your ISP gives you.  You do not need a
router with NAT, in fact if you are going through a router on your
local side, you want to make sure that it has PPTP or IPSec
passthrough turned on.  Once you have connected with your VPN client,
you should be able to do an IPCONFIG /ALL from the command prompt to
see your new VPN IP address.  If it is not an IP that is allowed to
traverse the network to the remote sites, then you will have to have
the administrator either add the address pool from which you received
your address to the list of addresses that are allowed across the VPN
links, or have them set the VPN DHCP pool to be addresses that are
already allowed across the links.

You don't want your client to ignore the IP address from your ISP, it
is the IP address that is communicating with the external interface of
your companies firewall, router, VPN concentrator, etc...  The address
you receive after the tunnel is setup is used solely for traffic
across the tunnel, unless it is set as your default gateway, in which
case all traffic heading to a network to which you are not directly
connected to will also be directed to the tunnel (ie. internet
traffic)  Basically, you need the address your ISP gave you to route
between your computer and your company, the VPN 'tunnels' on top of
that existing connection.

Network Address Translation will take the ISP allocated IP address and
translate it into an internal IP address, allocated by the DHCP or
other IP address allocator.  This is not from the client side, it is
done at the companys VPN connection, in fact generally after the VPN
connection has connected.  Port Address Translation is somewhat
different, allocating external port address to internal IP's depending
on function, thus allowing several internal IP addresses to
effectively use one external IP address.

BB

PS - Sorry if I confused before, where I said, "you will probably need
a router with NAT" 'you' should have been read as 'the company'.  Also
you say that this the current VPN configuration is 'site to site',
does that mean this is a permanent connection between two or more
LANS?