According to this config you should be able to ping hosts on the DMZ and the internet from the inside. But for some reason, you will never be able be able the DMZ or outside interface of pix from the inside. or the other way round.
First make sure that the hosts definately respond to pings (ping them from the local lan).
If they do, there is only one explanation: a slight pix mulfunction, so to say. I had a simmilar problem once. I configured everything correctly but still it didn't work. After a reboot it worked fine. but it did start to work. From what you are saying it doesn't work for a longer time and that is strange :)
Try to remove and reapply the ACL, reboot etc.
In software 7.0 and higher you can enable icmp inspection which would allow to pings to come back event without the access-list.
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...