Hi,
Everything seems to be fine with regards to the ASA configurations as the connections goes through just fine.
Are you sure that the default gateway of the server you are trying to reach is set to use the ASA "inside" interface as its gateway?
I am not sure have you completely replaced the old device with the ASA and did the old device have the same gateway IP address on its "inside" interface.
You should go to the Monitor -> Logging section of the ASDM and attempt the connection from the Internet to the server and see what the logs say.
- Jouni