Regarding your NAT problems you didn't mention what type of router you have connected to ISP. Is it Cisco or another vendor? Can you provide configuraion of your router?
Next, because you are able to connect to ASA from its outside network so problem will be probably on router side. As you mentioned in subject probably you have NAT problem. Whe you do NAT on touter so NATed PUBLIC IP address is ASA outside interface? Or do you perform PAT?
If possible please post configuration of your ASA box.
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...