If you have enabled split tunneling, then the Internet would not work through the VPN.
Moreover, Internet ass such can ot work through VPN, even if you disable split tunnel, because PIX 6.x code is not able to redirect the traffic on any of its interface. The capapbility was introduced in PIX 7.X code. PIX 506 ca not be upgraded to 7.X code.
The only two options you have right now are:
1: Either enable split tunneling, that way Internet traffic will go out unencrypted.
2: Or you can put a proxy server in inside subnet of PIX, and point the VPN client's browser to that proxy server ip address. This would however work for http traffic only.
Table of ContentsIntroductionVersion HistoryPossible Future
UpdatesDocuments PurposeNAT Operation in ASA 8.3+ SectionsRule Types
Network Object NATTwice NAT / Manual NATRule Types used per SectionNAT
Types used with Twice NAT / Manual NAT and Network Obje...
Table of Contents Introduction:This document describes details on how
NAT-T works. Background: ESP encrypts all critical information,
encapsulating the entire inner TCP/UDP datagram within an ESP header.
ESP is an IP protocol in the same sense that TCP an...