The Access-rules should be similar to what you have on the ASA version 8.3+. You do not need a NAT to go from inside to DMZ. You can however add a NAT exempt to exempt inside to DMZ traffic from any translation.
DMZ to outside would require an Auto NAT rule. Also, an ACL would be needed from Outside to DMZ to allow internet users to access your public DMZ servers.
It would be good if you can show us an example of what you have configured and what is not working.
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