From what i gather from the info you provided you are saying that the private LAN can not talk to the Internet. If you can ping the PIX from the Concentrator and from the Concentrator to any LAN Clients, I would figure it to be some sort of routing issue on the Concentrator.
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First off, do a traceroute from a LAN client to see where it stops
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here are some things to consider
is the private lan's default Internet route through the VPN Concentrator, then the PIX?
or is it going straight to the PIX on it's (Inside) interface ? if so, Can you ping the PIX (inside) interface from a LAN client?
do you have the correct default gateways configured on the clients?
do you have the routes configured on the Concentrator (default route 0.0.0.0 pointing out the Concentrator's public interface toward the PIX's DMZ interface IP)?
do you have 'setroute' configured on the PIX default route to 0.0.0.0?
you say that the PIX gets it's "static" IP thru PPPoE (???)